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BL    240    .C65    1893 

Cooke,    Josiah  Parsons,    1787 

1880. 
The   credentials   of    science 


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THE   CREDENTIALS    OF    SCIENCE 
THE   WARRANT   OF    FAITH. 


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Credentials  of  Science 


777£    WARRANT    OF   FAITH. 


BY 


JOSIAH   PARSONS   COOKE,  LL.D., 

ERVING    PROFESSOR     OF    CHEMISTRY    AND    MINERALOGY    IN 
HARVARD    UNIVERSITY. 


SECOND   EDITION. 


NEW    YORK: 

D.    APPLETON    AND    COMPANY. 

1893. 


Copyright,  1888, 
Bv  ROBERT  CARTER  AND   BROTHERS. 

Copyright,  1893, 
By  JOSIAH  P.  COOKE. 


IN   MEMORIAM 


'QUI  docti  fuerint  fulgebunt  quasi  splendor  firmamenti; 

ET   QUI    AD   JUSTITIAM    ERUDIUNT   MULTOS,    QUASI 
STELLA    IN    PERPETUAS   yETERNITATES." 


PREFACE   TO    SECOND   EDITION. 


THE  subject  of  this  volume  was  first  developed 
by  the  author  as  a  course  of  lectures  at  the 
invitation  of  the  Union  Theological  Seminary  of 
New  York  City,  and  the  lectures  were  delivered  in 
the  Adams  Chapel  of  the  Seminary  during  the  early 
spring  of  1887,  the  course  of  eight  lectures  closing 
on  Easter  Eve.  The  course  was  given  on  a  founda- 
tion established  by  Mr.  Zebulon  Stiles  Ely  to  sup- 
port a  lectureship  on  the  Evidences  of  Christianity. 
The  material  was  subsequently  considerably  ampli- 
fied, and  delivered  as  a  course  of  twelve  lectures 
before  the  Lowell  Institute  of  Boston,  closing  on 
Christmas  Eve  of  the  same  year.  The  lectures  have 
been  printed  as  thus  extended,  although  in  some 
cases  the  limitations  of  a  lecture  hour  compelled 
a  division  of  subjects,  which  are  here  united  under 
the  same  heading,  thus  reducing  the  number  of 
chapters  in  the  book  to  ten. 

The  motive  of  the  work  is  indicated  by  the  title, 
the  chief  argument  being  that  the  popular  objec- 
tions to  Christian  beliefs  might  be  urged  with  equal 
force   against  each  of  the  predominant  systems  of 


Vlll  PREFACE   TO   SECOND   EDITION. 

science  of  the  present  day,  and  are  the  necessary- 
result  of  the  limitations  of  our  human  knowledge  ; 
that  so  far  from  proving  the  inconsequence  of  our 
religious  beliefs,  the  oppositions  so  greatly  magnified 
plainly  point  to  a  condition  in  which  the  limitations 
that  now  narrow  our  vision  will  be  removed.  In 
following  out  this  argument  the  author  has  discussed 
the  basis  of  scientific  systems ;  the  modes  of  thought 
distinguished  as  induction  and  deduction,  by  which 
general  principles  have  been  apprehended  and  their 
scope  constantly  widened  ;  the  significance  of  the  so- 
called  laws  of  Nature ;  the  validity  of  the  prevailing 
theories  or  systems  of  science ;  and  the  predominant 
principles  of  scientific  thought. 

By  the  terms  of  the  appointment  to  the  Ely  Lec- 
tureship the  copyright  of  this  book  was  vested  in 
the  Union  Theological  Seminary,  and  the  first  edition 
was  published  by  Robert  Carter  and  Brothers,  under 
the  auspices  of  the  Seminary ;  but  after  that  firm 
retired  from  business,  the  directors  of  the  Seminary, 
by  vote  at  a  meeting  held  on  November  10,  1891, 
transferred  the  copyright  to  the  author,  who  has 
carefully  revised  the  work  for  a  new  edition.  No 
important  changes  have  been  made  in  the  form  of 
the  argument  or  in  the  mode  of  presentation,  but 
the  text  has  been  revised,  and  misprints,  as  far  as 
discovered,  corrected. 

Cambridge,  April  22,  i8gj. 


CONTENTS. 


Lecture  Page 

I.    The  Argument  of  Natural  Theology    .     .  i 

II.     Preparing  the  Way 29 

III.  The  Induction  of  Newton 59 

IV.  Deduction 93 

V.    Examples  of  Scientific  Investigation     .     .  127 

VI.    Laws  of  Nature 158 

VII.     Determinate  and  Indeterminate  Laws  .     ■  184 

VIII.    Theories  or  Systems  of  Science     ....  209 

IX.     Predominant    Principles   of    Scientific 

Thought 260 

X.    The    Systems    Compared.  —  Religion   and 

Science 289 


The  Credentials  of  Science 

THE   WARRANT  OF  FAITH. 


LECTURE   I. 

THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

NATURAL  Religion  is  as  old  as  man's  conscious- 
ness of  dependence,  and  Natural  Theology  is 
coeval  with  literature.  Its  fundamental  arguments 
were  urged  by  the  Greek  and  Roman  philosophers, 
and  the  illustrations  of  the  subject  by  Galen  have 
scarcely  been  equalled  in  modern  times.  During 
the  last  two  centuries  works  on  natural  theology 
have  formed  a  conspicuous  feature  in  English  litera- 
ture, —  in  consequence  chiefly  of  several  pious  foun- 
dations which  have  provided  for  the  discussion  of  the 
subject  at  stated  intervals.  These  works  have  as  a 
rule  been  written  in  a  popular  style,  and  have  dealt 
with  illustrations  of  old  arguments  rather  than  with 
the  arguments  themselves.  They  have  served  an  ex- 
cellent purpose  by  keeping  before  the  popular  mind 
the  ever  accumulating  mass  of  evidence  of  skill  and  of 
plan  which  nature  offers,  and  by  exhibiting  the  reli- 
gious aspects  of  scientific  facts  and  theories.     Unfor- 


2    THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

tunately  they  have  often  been  open  to  criticism,  and 
too  frequently  have  justified  the  contempt  into  which 
teleology  has  so  generally  fallen. 

A  recent  writer,  in  his  "  Critique  of  Design  Argu- 
ments," x  has  done  an  excellent  work,  not  only  by  fix- 
ing attention  on  the  arguments,  but  also  by  furnishing 
a  carefully  prepared  synopsis  of  all  the  important 
writings  bearing  on  natural  theology  from  the  earliest 
times.  But  while  freely  admitting  the  justice  of  this 
writer's  criticism  in  many  respects,  even  when  we  our- 
selves have  fallen  under  the  ban,  we  cannot  concur 
with  him  either  in  his  general  estimate  of  design  argu- 
ments, or  in  the  essential  character  of  the  distinction 
which  he  seeks  to  draw  between  the  argument  from 
general  plan  and  the  so-called  argument  from  design. 
This  last  phrase  has  become  one  of  the  universal 
terms  of  our  language,  and  it  is  not  to  be  supposed 
that  acute  Scotch  logicians  like  Dugald  Stewart  and 
Reid  overlooked  the  obvious  begging  of  the  question 
which  a  precise  definition  of  the  words  would  involve. 
There  has  been  undoubtedly  as  frequent  misuse  of 
language  in  essays  on  natural  theology  as  in  similar 
popular  expositions ;  but  much  of  this  has  resulted 
from  the  necessities  of  the  case. 

In  popular  discourse  language  cannot  be  used  with 
the  precision  of  mathematical  terrn.3,  and  often  a 
hypercritical  spirit  defeats  the  main  object  of  the 
teacher.  Singular  as  it  is,  the  more  a  man  knows,  the 
more  difficult  it  becomes  to  present  a  subject  in  lan- 
guage that  can  be  easily  comprehended.    The  teacher 

1  Critique  of  Design  Arguments,  by  L.  E.  Hicks.  New  York. 
Charles  Scribner's  Sons,  1883. 


DESIGN   SUPPOSES  A  DESIGNER. 


is  hampered  by  his  knowledge  of  the  limitations  to 
the  general  propositions  he  enunciates,  and  he  is 
forced  to  avail  himself  of  all  the  latitude  which  the 
most  liberal  interpretation  of  language  will  allow. 
No  one  who  has  not  had  the  experience  knows  how 
difficult  it  often  is  to  reconcile  exact  accuracy  with 
that  concise  statement  which  is  one  of  the  essential 
conditions  of  effective  teaching;  and  the  intended  pur- 
port of  rhetorical  writing  can  always  be  misrepre- 
sented by  the  quotation  of  isolated  passages. 

When  an  able  theologian  writes,  "  Design  supposes 
a  designer,"  it  is  reasonable  to  infer  that  he  does  not 
intend  to  involve  his  readers  in  the  logical  absurdity 
of  an  identical  proposition,  but  simply  intends  to  de- 
clare the  undoubted  fact,  that  a  multitude  of  relations 
in  nature  suggest  to  the  mind  of  man  an  intelligent 
author. 

The  confusion  implied  in  this  and  in  similar  phrase- 
ology arises  from  an  attempt  to  gauge  such  reason- 
ing by  the  rules  of  deductive  logic.  Man  has  not 
risen  to  knowledge  of  Divine  things  by  deduction  but 
by  induction.  These  things  always  have  been,  and 
always  will  continue  to  be  to  the  logical  Greeks  of 
every  age  foolishness,  and  so  long  as  the  theologian 
cherishes  the  conceit  that  the  Godhead  can  be  dem- 
onstrated, he  cannot  hope  to  escape  from  the  web  of 
logical  fallacies  which  his  argument  must  involve. 

The  knowledge  of  God  has  come  to  man  through 
nature  precisely  in  the  same  way  as  the  generaliza- 
tions of  science,  and  is  subject  to  the  same  limitations 
and  carries  the  same  conviction  as  all  general  truths. 
Man  knows  God  by  the  same  means  and  through  the 


4    THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

same  sources  that  he  knows  the  principles  of  gravita- 
tion, heat,  and  electricity.  In  each  case  an  assumed 
energy  acting  through  special  channels  under  definite 
laws  is  the  best  explanation  he  can  form  of  a  certain 
class  of  phenomena.  So  also  the  assumption  of  an 
Intelligent  Will,  with  power  to  create  and  power  to 
sustain,  is  the  commonly  received  explanation  which 
man  has  formed  of  the  origin  and  continuance  of  this 
universe  in  which  he  dwells. 

The  fundamental  principles  of  science  may  be  said 
to  be  suggestions  of  nature  confirmed  by  experience. 
When  once  conceived,  we  can  often  deduce  from  a 
general  principle,  mathematically  or  otherwise,  a  host 
of  inferences  which  observation  substantiates.  This 
indeed  is  the  normal  way  by  which  our  knowledge  of 
nature  is  enlarged ;  and  such  deductions,  verified  by 
experience,  furnish  the  strongest  confirmation  of  the 
truth  of  the  principle  with  which  we  started.  But  the 
principle  itself  was  no  deduction,  it  was  a  suggestion 
of  nature ;  and  this  is  all  we  know  of  its  origin.  We 
may  seek  to  study  the  conditions  and  circumstances 
under  which  such  suggestions  have  come  into  the 
minds  of  the  favored  men  of  the  race,  but  we  get  no 
nearer  to  the  source. 

Among  essential  conditions  we  at  once  recognize 
a  familiar  acquaintance  with  nature,  and  a  powerful 
but  well  regulated  imagination.  We  also  readily  trace 
the  influence  of  analogies,  and  even  of  accidental  asso- 
ciations. We  easily  see  anthropomorphic  elements 
in  such  conceptions ;  but  all  these  things  are  merely 
accessories  to  a  mental  process  of  which  the  discoverer 
himself  can  give  no  clear  account,  as  the  trivial  stories 


THE   CONCEPTION   OF   GOD   AN   INDUCTION.  5 

of  swinging  lamps  and  falling  apples  so  plainly  show. 
It  is  a  mental  faculty  which,  though  in  its  highest 
manifestation  only  known  to  a  few  highly  gifted  men, 
is  in  some  small  measure  within  the  experience  of 
every  student  of  nature.  To  such  students  the 
method  seems  perfectly  natural,  even  when  they  may 
not  be  able  to  discover  its  elements.  Many  philoso- 
phers, like  Bacon,  have  attempted  to  analyze  the 
method,  and  have  named  it  "  induction ;  "  but  few  of 
those  who  are  in  the  habit  of  using  the  method  would 
recognize  the  mechanism  that  has  been  described. 
The  so-called  induction  resembles  inspiration,  and 
the  loftiest  inspiration  seems  to  be  only  the  same  fac- 
ulty of  mind  more  highly  developed. 

As  are  the  fundamental  principles  of  science,  so  is 
the  conception  of  God  a  suggestion  of  nature  con- 
firmed by  experience.  It  is  an  induction  which  com- 
mands belief,  not  a  deduction  which  compels  consent. 
This  difference  between  inductive  and  deductive  truth 
does  not  depend  upon  the  degree  of  certitude,  but  on 
the  completeness  of  knowledge.  The  highest  truths 
can  be  known  only  in  part,  and  it  is  such  truths  that 
are  reached  by  induction.  Thus  alone  can  men  "  rise 
on  stepping-stones  of  their  dead  selves  to  higher 
things."  Moreover,  of  such  truths  certitude  of  con- 
viction comes  only  with  experience.  Christ  said  "  If 
ye  do  my  will  ye  shall  know  of  the  doctrine  "  and  the 
principle  thus  announced  applies  to  all  inductive 
truths. 

It  is  only  beliefs  thus  attested  which  command  the 
enthusiasm  of  men.  For  such  beliefs  alone  will  men 
sacrifice  their  lives.    The  deductions  of  Geometry  are 


RELIGION   AND   CHEMISTRY. 


great  truths  fully  comprehended  ;  but  how  inconceiv- 
able, a  martyr  to  the  theorem  of  Pythagoras !  And 
there  never  would  have  been  a  martyr  to  religious  be- 
liefs, if  these  verities  could  have  been  reached  by  de- 
duction,—  in  a  word,  could  have  been  demonstrated. 

Regard  now  the  fundamental  truth  of  natural  re- 
ligion as  an  induction,  comprehended  only  in  part, 
but  having  all  the  certitude  which  the  experience  of 
the  ages  has  given,  and  your  natural  theology  becomes 
a  system  which  is  not  only  consistent  throughout,  but 
which  harmonizes  with  all  knowledge.  Attempt,  how- 
ever, to  claim  for  this  truth  deductive  demonstration, 
and  you  at  once  involve  your  system  in  contradictions, 
and  miss  the  very  certitude  you  are  seeking  to  secure. 

More  than  twenty-five  years  ago  the  writer  de- 
livered a  course  of  lectures  at  Brooklyn,  on  the  Gra- 
ham Foundation,  in  which  the  position  just  defined 
was  distinctly  taken.  These  lectures  were  subse- 
quently published,  and  the  book  is  well  known  under 
the  title  of"  Religion  and  Chemistry,  or  Proofs  of  God's 
Plan  in  the  Constitution  of  the  Atmosphere."  The 
lectures  were  written  for  a  popular  audience,  and  there- 
fore in  a  rhetorical  form,  and  it  would  be  easy  to  mis- 
represent the  argument  by  a  quotation  of  isolated 
passages ;  but  no  one  who  actually  reads  the  book 
can  mistake  either  the  intentions  of  the  writer  or  the 
spirit  of  his  work.  No  one  could  have  been  more 
dissatisfied  with  the  work  than  the  author  himself, 
and  for  this  reason  he  suffered  the  book  to  remain 
out  of  print  for  many  years;  and  when  after  repeated 
requests  from  clerical  friends  the  work  was  revised  for 
the  recent  edition,  the  expository  and  rhetorical  form 


CONFLICT   BETWEEN   SCIENCE   AND   THEOLOGY.    J 

was  retained  simply  because  in  the  judgment  of  these 
friends  the  usefulness  of  the  book  depended  in  no 
small  measure  on  its  popular  style.  Thus  called  upon 
to  review  what  was  written  at  a  time  when  it  might  be 
expected  that  logic  should  be  somewhat  blinded  by  en- 
thusiasm, the  writer  could  find  nothing  in  the  tenor  or 
spirit  of  the  work  that  he  desired  to  change;  and  the 
general  argument  appears  to  him  still,  as  it  did  at  first, 
unanswerable. 

Now,  however,  that  I  am  invited  to  address  the 
members  of  this  influential  theological  seminary  on 
the  same  general  subject,  I  feel  that  the  best  service 
I  can  render  is  to  present  the  same  argument  in  a 
more  methodical  and  compact  form,  —  a  form  in 
which  its  strength  will  better  appear,  and  its  weak- 
ness, if  any,  will  be  more  conspicuously  exposed. 
With  no  desire  to  magnify  my  office,  I  cannot  but 
feel  that  the  subject  under  discussion  is  one  of  great 
importance  to  theological  students.  It  is  the  ground 
on  which  the  conflict  between  science  and  theology 
has  always  been  fought.  Whatever  may  have  been 
the  incidental  advantages,  no  one  can  question  that  the 
conflict  itself  is  a  great  evil.  Is  it,  indeed,  necessary 
that  the  promulgation  of  every  important  doctrine  of 
science  should  be  followed  by  a  partial  eclipse  of 
faith,  like  that  through  which  so  many  minds  have 
recently  been  passing?  Brought  as  I  have  been  into 
sympathy  with  the  advocates  on  both  sides,  I  believe 
I  am  in  a  position  to  form  an  impartial  judgment; 
and  while  fully  recognizing  the  narrowness  and  evil 
spirit  which  men  even  of  large  knowledge  have  often 
exhibited,  I  feel  constrained  to  express  the  opinion  that 
the  clergy  are  largely  responsible  for  the  bad  effects 


8    THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

of  the  controversy.  Remember  that  science  is  para- 
mount in  its  own  sphere,  that  its  methods  are  legiti- 
mate, and  its  only  object  is  truth ;  and  be  assured 
that  if  any  one  of  its  devotees  is  irregular  in  his 
methods,  or  false  to  his  profession,  his  own  associates 
will  be  the  first  to  criticise  and  condemn  his  errors. 
Moreover,  the  doctrines  of  science  are  held  with 
great  jealousy;  and,  although  the  evils  of  partisan- 
ship are  as  great  in  scientific  controversies  as  else- 
where, the  doctrines  themselves  will  stand  or  fall 
solely  on  their  own  merit  in  the  end.  Once  attested 
they  cease  to  be  safe  subjects  for  the  uninitiated  to 
discuss,  and  much  less,  proper  objects  to  anathema- 
tize. I  can  assure  you  that  there  have  been  times 
when  the  obligation  which  the  church  enjoins  to  hear 
sermons  has  been  a  painful  duty  to  one  who  holds 
the  truth  in  reverence,  and  desires  also  to  reverence 
the  defenders  of  the  "  faith  once  delivered  to  the 
saints."  I  cannot  but  believe  that  if  the  clergy 
understood  more  fully  the  true  relations  of  scientific 
doctrines,  and  saw  clearly  that  the  fundamental  postu- 
late of  theology  rests  on  the  same  basis,  they  would 
be  more  patient  with  the  inevitable  friction  which 
attends  the  progress  of  truth  as  well  as  the  coming 
of  the  kingdom. 

In  discussing  the  broad  subject  of  natural  theology 
the  limitations  of  my  own  studies  must  necessarily 
constrain  me  to  confine  myself  to  those  arguments 
which  may  be  drawn  from  the  facts  of  external  na- 
ture; and  this  I  shall  do  without  in  the  least  under- 
valuing the  purely  ontological  arguments  based  on 
the  equally  definite  facts  of  consciousness.     But  let  it 


DEVELOPMENT   OF  THE   CONCEPTION   OF   GOD.      9 

also  be  clearly  understood  that  I  shall  regard  as  a 
part  of  the  phenomena  of  nature  the  undoubted  his- 
torical facts  of  Christianity,  as  well  as  the  clearly 
established  facts  connected  with  other  religions ;  and 
in  my  opinion  the  evidences  of  natural  theology  are 
most  incomplete  when  these  all-important  phenom- 
ena are  left  out  of  view.  Of  course  such  facts  will 
be  here  studied  in  their  objective,  and  not  in  their 
subjective  aspect. 

By  considering  the  development  of  the  conception 
of  God  in  the  mind  of  man,  I  think  we  can  gain  some 
insight  into  the  nature  of  the  mental  process  by 
which  the  conception  is  reached,  and  in  the  same 
way  that  by  the  study  of  embryology  we  gain  a 
better  knowledge  of  animal  structure.  There  can  be 
no  question  that  there  are  certain  uniform  stages  in 
the  order  of  this  development,  both  in  the  history  of 
the  race  and  in  the  education  of  each  individual 
man.  This  very  uniformity  under  such  diverse  con- 
ditions plainly  shows  that  the  conception  is  not  the 
accident  of  circumstances,  but  the  normal  product 
of  the  human  mind  under  its  environment.  We  do 
not  call  it  intuitive,  because  we  do  not  care  to  raise 
the  question  that  the  word  intuition  suggests,  —  a 
question  with  which  we  have  no  immediate  concern. 
But  whether  the  result  of  intuition  or  of  inspiration, 
or,  more  probably,  of  both  of  these  ideal  functions  of 
the  mind,  acting,  as  we  have  said  before,  under  its 
environments,  the  conception  is  unquestionably  as 
spontaneous  as  it  is  real. 

In  discussing  the  development  of  the  fundamental 
conceptions  of  all  religions,  it  is  not  necessary  for  us 


10        THE   ARGUMENT   OF   NATURAL  THEOLOGY. 

to  enter  upon  any  abstruse  questions  of  ethnology, 
archaeology,  or  philology,  although  all  this  learning 
might  be  brought  to  bear  on  the  subject.  The  gen- 
eral conclusions  with  which  alone  we  shall  have  to 
deal,  are  so  patent  that  they  will  be  accepted  by 
every  one,  and  this  circumstance  alone  shows  how 
fundamental  are  the  phenomena  we  are  considering. 

When  the  child  first  becomes  conscious  of  his  free 
will  he  finds  that  will  opposed  by  other  wills  like  his 
own,  and  we  all  know  what  an  essential  condition 
of  education  is  the  conflict  which  results.  In  our 
short-sightedness  how  greatly  do  we  regret  this  con- 
flict, how  earnestly  seek  to  avoid  it,  and  how  often 
do  we  shun  the  responsibility  it  involves ;  and  yet 
how  fully  do  we  recognize  that  no  strength  of  char- 
acter, no  force  of  will,  no  power  of  intellect,  no  assur- 
ance of  faith,  can  be  gained  except  by  conflict ;  how 
often  only  after  repeated  disasters  are  these  virtues 
secured,  and  how  forcibly  does  some  of  the  most 
beautiful  imagery  of  our  language  illustrate  this 
truth. 

As  to  every  child,  so  with  freedom  of  the  will 
there  must  have  come  at  some  first  time  to  primeval 
man  the  conception  of  an  opposing  will ;  and  the 
warfare  then  began  through  which  the  race  has  been 
educated.  Admit  that  this  conflict  is  but  a  continu- 
ation of  the  struggle  for  existence  which  began  with 
life,  yet  now  certainly  the  struggle  involves  for  the 
first  time  conscious  personality,  and  the  mysterious 
knowledge  of  good  and  evil,  so  inseparably  associ- 
ated with  that  freedom  which  makes  us  responsible 
beings. 


THE  ARGUMENT  OF   MIGHT.  i  i 


Through  the  conflicts    of  his  will  man    acquired 
his   first  conception  of  power,  the  earliest  measure 
of  his  own  strength.     In  his  fellow-men  he  at  once 
recognized  powers  commensurate  with  his  own,  to 
which  he  was  frequently  forced  to  yield,  but  which 
he  could  often  overcome ;   and  with  such  powers  he 
from  the  first  associated  personality.     But  it  required 
only  a  short  experience  with  nature  to  force  upon 
him  the  knowledge  that  he  was  under  the  control  of 
powers  vastly  superior  to  those  of  men,  which  he 
could  not  withstand,  and  by  which  his  fellows  were 
frequently  overwhelmed,  —  powers  so  mighty  and  so 
hidden  that  he  quailed  and  trembled  before  them. 
As  he  knew  power  only  as  an  attribute  of  personality, 
he   ascribed    the    powers   of  nature    to    mighty  and 
exalted  personages  capable  of  such  vast  effects ;   and 
hence  came  man's  first  conception  of  God.    The  God 
thus  conceived  was  merely  the  God  of  might,  the 
God  who  rules  in  the  tempest  and  directs  the  thun- 
derbolts, the  God  who  rejoices  in  war  and  carnage. 
Moreover,  these  powers  did  not  seem  to  be  wielded  by 
a  single  person.     Man  was  still  far  from  the  concep- 
tion of  a  Jehovah ;   but  as  he  was  opposed  by  many 
persons  so  his  fancy  filled  the  heavens  with  a  host  of 
warring  gods. 

It  is  not  our  purpose  to  sketch  the  numberless 
fanciful  forms  which  under  different  associations  the 
early  conception  assumed.  We  desire  only  to  em- 
phasize the  fact  that  the  earliest  conception  of  God 
was  that  of  a  God  of  Might,  and  that  this  conception 
came  to  the  savage  as  an  obvious  suggestion  of  na- 
ture.    It  was  an  induction  from  observed  facts;  and 


12   THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

simple  and  obvious  as  the  induction  was,  the  mental 
process  by  which  it  was  reached  differed  in  degree 
only,  not  in  kind,  from  the  inductions  of  modern 
science. 

Such  inductions  do  not  of  course  bring  with  them 
their  credentials ;  but  in  so  far  as  they  embody  truth, 
they  become  accredited  through  experience,  and 
chiefly  in  two  ways :  first,  by  their  universality,  that 
is,  by  coming  to  many  persons  independently,  thus 
showing  that  they  are  in  harmony  with  the  constitu- 
tion of  the  human  mind ;  and  secondly,  by  their 
permanency  in  retaining  their  hold  on  men,  indicat- 
ing that  they  have  stood  the  test  to  which  they  have 
been  exposed,  and  by  which  they  have  been  tried. 

The  primitive  inductions  of  men  must  necessarily 
be  very  partial  truths,  and  the  grain  of  truth  is  con- 
stantly so  incrusted  with  error  that  it  is  with  difficulty 
discovered ;  but  I  feel  persuaded  that  beliefs  which 
are  long  held  in  reverence  owe  their  power  to  this 
grain  of  truth,  however  small. 

A  most  striking  feature  of  inductions,  by  which 
they  are  plainly  distinguished  from  deductions,  is  to 
be  found  in  that  inductions  are  progressive,  and 
become  clarified  with  experience.  A  deduction  is 
demonstrative,  and  if  the  premises  are  correct,  the 
conclusion  naturally  follows.  There  is  no  question 
as  to  degree,  no  room  for  doubt  except  as  regards 
the  premises  of  the  argument.  An  induction,  how- 
ever, may  have  every  possible  degree  of  certitude, 
from  an  unverified  conjecture  to  a  law  of  nature  con- 
firmed by  experience.  Moreover,  in  the  progress  of 
knowledge  it  has  been  constantly  the  case  that  the 


INDUCTIONS   BECOME   SLOWLY   CLARIFIED.        1 3 

conjecture  has  appeared  as  a  law  only  after  a  slow 
clarifying  process.  As  the  dregs  have  settled  from 
the  intellectual  medium,  the  truth  has  been  seen  in 
ever  clearer  outlines ;  its  essential  features  have  be- 
come evident,  while  the  grosser  aspects  of  the  orig- 
inal crude  conception  have  disappeared.  Such  has 
been  the  uniform  history  of  the  great  generalizations 
of  science,  and  through  such  a  clarifying  process  are 
most,  if  not  all,  of  them  still  passing.  Possibly  in 
a  very  few  cases  the  truth  even  now  appears  in  all 
its  simplicity;  but  there  can  be  no  question  that  in 
the  case  of  most  of  the  fundamental  principles  of 
modern  science  of  which  we  feel  so  proud,  and  which 
have  been  such  valuable  guides  in  the  study  of  na- 
ture, the  truths  they  embody  are  still  only  seen  as 
in  a  glass  darkly.  It  has  been  the  privilege  of  a  few 
gifted  minds  to  see  the  truth  of  the  inductions  they 
have  made  generally  recognized  during  their  life  on 
earth,  but  as  a  rule  so  many  minds  have  concurred  in 
developing  these  general  truths  that  they  must  be  re- 
garded as  the  product  of  the  age,  rather  than  as  the 
gift  of  any  one  man  to  the  knowledge  of  the  world. 

These  features  of  scientific  generalizations  are  strik- 
ingly characteristic  of  the  fundamental  religious  con- 
ception, which  is  also,  as  we  have  claimed,  an  induc- 
tion from  observed  facts.  As  first  seen  through  the 
mists  of  barbarism,  God  was  a  Moloch,  or  a  Thor,  or 
at  best  a  Jupiter;  but  as  in  proportion  to  his  men- 
tal growth  man's  spiritual  vision  became  clearer,  the 
image  became  ever  more  definite,  more  beautiful, 
and  more  lovely.  It  is  not  our  purpose  to  trace 
the   connection   between  the  thousands  of  fantastic 


14       THE   ARGUMENT   OF  NATURAL   THEOLOGY. 


shapes  which  the  first  crude  shadowy  form  assumed, 
in  the  history  of  different  peoples,  but  we  must  mark 
four  important  stages  of  the  conception,  that  are  asso- 
ciated with  different  phases  of  the  argument  of  nat- 
ural theology. 

It  was  a  very  important,  although  doubtless  a  very 
early  advance  in  the  progress  of  our  race,  when  men 
first  invented  weapons  and  tools,  in  order  to  apply 
their  brute  strength  more  effectively,  or  direct  it  to 
more  useful  ends.  By  the  use  of  tools  primeval  man 
was  most  markedly  distinguished  from  all  the  ani- 
mals with  which  he  was  associated,  including  the 
highest  anthropoids,  from  some  of  whose  progenitors 
man  is  supposed  to  have  descended. 

No  one  has  claimed  that  even  the  rudest  tools  were 
ever  made  by  anthropoids,  however  close  their  re- 
semblance to  man  ;  and  the  appearance  of  stone  im- 
plements in  the  strata  marks  the  introduction  of  man 
upon  the  earth  with  remarkable  sharpness.  There 
seems  to  be  here  a  most  striking  break  of  continuity, 
which  the  doctrine  of  gradual  evolution  has  not  hith- 
erto explained.  The  bones  which  we  invariably  find 
with  these  rude  tools  are  those  of  well  developed 
men,  oftentimes  with  skulls  at  least  as  capacious  as 
our  own. 

However  the  evolutionists  may  explain  these  note- 
worthy facts,  there  can  be  no  question  that  tools, 
even  in  their  most  primitive  form,  are  proofs  of  a  de- 
gree of  intelligence  which  did  not  appear  on  earth 
until,  outwardly  at  least,  man  had  become  essentially 
the  same  creature  that  he  is  to-day.  In  proportion 
as  man  has  risen  in  the  scale  of  intelligence  he  has 


INTELLIGENT   USE.  1 5 

displayed  an  ever  increasing  ingenuity  in  the  inven- 
tion of  tools  ;  and  the  printing-press,  the  power-loom, 
the  steam-engine,  the  electric  telegraph,  are  the  tools 
of  our  civilization,  as  the  flint  arrow-heads  and  stone 
axes  were  those  of  primeval  man. 

Obviously,  all  tools  or  other  implements  are  evi- 
dences of  intelligence.  If  now  we  inquire  on  what 
basis  this  evidence  rests,  I  think  it  will  be  found  to 
depend  on  the  fitness  of  these  implements  for  an  in- 
telligent use.  We  use  the  word  "  implements  "  here 
in  the  broadest  sense,  for  any  utensils,  even  orna- 
ments, wrought  for  a  specific  use  ;  and  it  is  the  fitness 
of  such  implements  for  an  intelligent  use  which  consti- 
tutes the  evidence  of  intelligence  that  such  objects  as 
are  collected  in  an  archaeological  museum  afford.  It 
may  be  that  the  archaeologist  cannot  determine  the  use 
of  certain  objects,  but  even  such  objects  bear  marks 
of  having  been  wrought  with  tools,  whose  intelligent 
use  is  known,  and  must  therefore  be  classed  with 
them.  In  the  last  analysis  intelligent  use  is  the  funda- 
mental evidence  on  which  our  conclusion  as  regards 
the  intelligence  of  the  agency  which  fashioned  the  im- 
plements depends ;  and  the  fitness  of  the  implements 
for  such  use,  or  even  the  traces  of  tools  having  such 
fitness,  are  a  secondary  but  still  a  conclusive  evidence 
of  intelligence;  because  such  fitness,  or  traces,  dis- 
tinctly point  out  the  intelligent  use  for  which  the 
implements  were  made.  It  is  not  the  marks  of  the  in- 
scription which  are  the  fundamental  evidence  of  the 
intelligence  that  an  inscription  always  suggests,  but 
the  thought  which  these  marks  have  often  concealed. 
Before  the  Assyrian  characters  could  be  read   it  was 


I 6   THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

not  seriously  doubted  that  they  were  the  writings  of 
men,  because  they  bore  a  close  resemblance  to  such 
writings.  But  evidently  if  the  arrow-head  characters 
had  proved  to  be  simply  the  effect  of  natural  causes, 
like  the  crystal  outlines  on  a  slab  of  graphic  granite, 
such  markings  would  be  no  longer  any  evidence  of 
intelligence.  On  the  other  hand,  if  they  had  proved 
to  be  simple  ornamentations  they  would  still  be  evi- 
dences of  intelligence ;  and,  even  if  it  had  only  ap- 
peared that  they  had  been  cut  or  moulded  with  tools, 
however  rude,  they  would  likewise  be  evidences  of 
intelligence  through  the  intelligent  use  of  the  tools 
employed. 

In  discussing  this  question  we  cannot  be  too  care- 
ful constantly  to  bear  in  mind  that  it  is  the  intelligent 
use  of  tools  which  is  the  evidence  of  intelligence ;  and 
that  the  fitness  of  the  tools  is  also  a  proof  of  intelli- 
gence only  so  far  as  it  clearly  indicates  an  intelligent 
use.  It  is  not  necessary  in  this  connection  to  distin- 
guish the  fabrication  of  a  tool  from  its  use;  for  the 
fabrication  implies  the  use,  and  also  the  use  of  other 
tools,  from  the  most  complex  down  to  the  simplest 
tools  furnished  by  nature,  —  a  bamboo  from  the 
thicket,  a  stalk  of  flax  from  the  field,  or  a  sharp  stone 
from  the  brook.  It  may  often  be  that  a  tool  will  be 
found  better  adapted  for  some  other  use  than  for  the 
one  for  which  it  was  originally  made,  when  its  use  in 
the  new  relation  will  be  just  as  much  an  evidence  of 
intelligence  as  its  first  use. 

Every  one  has  heard  the  story  of  Timothy  Dexter, 
who,  in  his  absurd,  and  probably  not  very  truthful, 
personal  narrative,  says  he  made  a  successful  venture 


INTELLIGENT   USE.  1 7 


by  sending  a  cargo  of  warming-pans  to  the  West 
Indies,  where  they  were  found  to  be  admirably  fitted 
for  the  purpose  of  straining  sugar.  Evidently  the  use 
of  the  pan  for  straining  sugar  was  as  much  an  evi- 
dence of  intelligence  as  its  use  as  a  warming-pan ; 
but  the  fitness  of  the  tool  for  either  purpose  was  of 
value  as  evidence  only  so  far  as  it  indicated  an  intel- 
ligent use.  The  warming-pan,  however  admirably 
adapted  for  the  purpose,  was  not  designed  for  strain- 
ing sugar;  and  the  illustration,  whether  authentic  or 
not,  plainly  shows  that  in  human  relations  fitness 
proves  design,  that  is,  intelligence,  only  so  far  as  it 
indicates  intelligent  use.  In  the  relations  of  an  infin- 
ite being  who  knows  all  the  ends  from  the  beginning 
it  is  doubtless  otherwise ;  but  this  we  cannot  assume 
in  our  argument  from  design,  and  the  failure  to  make 
the  distinction  we  have  drawn  has  often  exposed  this 
argument  to  undeserved  contempt. 

Another  anecdote  illustrating  the  same  distinction 
has  the  advantage  of  being  certainly  true.  A  West 
India  planter  sent  to  his  overseer  from  New  York  a 
number  of  wheelbarrows,  by  whose  use  he  expected 
to  economize  labor  on  his  plantation.  They  were 
duly  received,  and  the  overseer  wrote  that  they  had 
been  found  to  be  very  useful ;  but  what  was  the  plant- 
er's surprise  on  returning  home,  to  see  the  negroes, 
after  shovelling  in  the  earth,  lift  the  barrows  on  to 
their  heads  and  march  off  with  the  load  in  their  old 
accustomed  way.  One  can  easily  see  that,  compared 
with  the  wicker  basket  previously  used,  the  wheel- 
barrows, even  thus  handled,  might  prove  a  saving  of 
labor,  and  can  recognize  a  low  intelligence  in  the 


I 8        THE   ARGUMENT   OF  NATURAL  THEOLOGY. 

negroes  who  accommodated  the  new  tool  to  their  old 
habits.  But  if  they  ever  thought  at  all,  those  negroes 
must  have  been  puzzled  by  the  wheel,  and  it  must  have 
presented  to  them  a  problem  of  very  much  the  same 
kind  that  the  much  discussed  rudimentary  organs 
offer  to  the  modern  teleologist.  Certainly,  the  wheel- 
barrow was  not  designed  to  be  carried  on  the  head, 
and  the  neglected  wheel  was  the  constant  witness  of 
this  fact;  but  the  ultimate  evidence  of  intelligence  in 
the  wheelbarrow  was  not  in  its  fitness  for  one  use  or 
for  the  other,  but  in  the  use  itself  which  the  fitness 
indicated.  The  fitness  is  important  solely  as  testify- 
ing to  the  intelligent  use. 

Our  early  ancestors,  however,  were  not  troubled  by 
the  analysis  of  any  such  distinctions  as  those  to  which 
we  resort,  to  justify  their  usually  correct  conclusions, 
however  much  they  may  have  erred  in  special  cases. 
They  associated  an  intelligent  personality  directly 
with  fitness,  wherever  found.  As  nature  offers  num- 
berless examples  of  fitness  vastly  more  wonderful  than 
that  displayed  by  any  human  tools,  they  ascribed  all 
such  relations  in  the  scheme  of  nature  to  the  wise  de- 
signs of  the  gods  whom  they  already  recognized  as 
wielding  the  powers  of  the  world.  From  the  brain 
of  Jupiter  came  Minerva  with  her  loom,  and  Vulcan 
with  his  forge;  and  from  such  beginnings  the  argu- 
ment from  design  has  been  handed  down  to  our  day. 
And  so  closely  have  men  always  associated  fitness  with 
personal  intelligence  that  in  all  languages  the  words 
expressing  these  relations  have  acquired  such  a  color- 
ing that  when  we  use  them  in  connection  with  teleo- 
logical  arguments  we  appear  to  beg  the  question  in 


FITNESS   IN   NATURE.  1 9 

the  simple  statement  of  the  case.  Such  words  as  "  de- 
sign," "contrivance,"  and  "adaptation,"  all  imply  a 
personal  agent;  and  in  looking  for  a  word  which 
would  express  simply  the  external  relation  from 
which  the  inference  of  personal  agency  is  drawn  we 
could  find  no  other  than  the  one  which  we  have  so 
continually  used,  namely,  fitness.  Largely  in  conse- 
quence of  the  misuse  of  terms  the  argument  from 
design  has  in  recent  years  fallen  into  such  disfavor 
that  the  very  word,  "  teleology,"  carries  with  it  a  sug- 
gestion of  opprobrium ;  and  yet  the  argument  is  in- 
trenched as  strongly  as  ever  behind  defences  which 
have  always  been  assaulted  in  vain ;  but  let  us  be 
sure  that  we  fully  know  where  the  strength  of  our 
position  lies. 

It  is  not  true  that  fitness  in  nature  in  any  limited 
relations  is  satisfactory  evidence  of  design,  and  the 
easy  "  reductio  ad  absurdum"  with  which  such  an 
assumption  is  readily  met  has  done  not  a  little  to  bring 
teleology  into  contempt.  As  has  been  shown,  this 
assumption  is  not  true  even  in  human  relations.  With 
the  tools  of  men  it  is  not  their  fitness  for  certain  uses 
but  the  intelligent  use  which  is  the  real  evidence  of  an 
intelligent  mind ;  and  far  less  in  nature  can  we  claim 
to  know  the  purposes  of  the  Original ;  and  if  we  at- 
tempt to  enforce  our  argument  by  the  plea  that  there 
can  be  no  use  which  Omniscience  could  not  have  fore- 
seen, as  before  intimated  we  directly  assume  the  very 
point  we  are  attempting  to  prove.  Nevertheless  the 
premises  of  our  argument  are  unquestioned ;  and 
these  are  the  relations  of  fitness  in  nature,  wonderful 
beyond  language  to  express,  intricate  beyond  thought 


20   THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

to  unravel,  sublime  beyond  imagination  to  conceive, 
useful  beyond  words  to  admire.  Now  men  have  been 
able  to  discover  but  one  satisfactory  explanation  of 
these  relations,  namely,  that  they  are  the  outcome  of 
an  intelligence  like  their  own,  only  of  an  immeasur- 
ably higher  order,  —  in  a  word,  that  they  were  created 
by  the  Jehovah  of  the  Bible.  We  must  not  claim 
that  we  have  here  logical  proof,  for  we  cannot  have 
any  such  demonstration.  But  we  have  something 
which  is  far  better  than  all  logical  proof,  something 
which,  while  it  carries  conviction,  inflames  our  imagi- 
nation, and  appeals  to  our  faith.  We  have  what  we 
technically  call  an  induction.  But  it  is  an  induction 
of  the  highest  order,  with  material  so  ample  and  ex- 
perience so  extended  as  to  leave  no  room  for  reason- 
able doubt. 

In  claiming  for  an  induction  the  validity  of  a  de- 
ductive demonstration,  we  compromise  the  whole 
strength  of  our  logical  position;  and  hence  many 
writers  on  natural  theology,  even  though  they  may 
not  have  attempted  to  analyze  the  argument  from  de- 
sign, have  discussed  the  examples  of  fitness  in  nature 
as  illustrations  of  an  admitted  principle,  and  not  as 
proofs  of  an  intelligent  author.  In  the  book  before 
referred  to,  we  ourselves  have  most  distinctly  and 
emphatically  maintained  this  attitude  towards  the 
subject.  It  must  be  remembered,  moreover,  that  on 
this  view  and  for  the  argument's  sake  such  discussions 
are  perfectly  legitimate ;  for  the  conviction  which  an 
induction  produces  depends  chiefly  on  the  extent  of 
the  field  which  it  grasps;  and  when  we  study  this 
great   induction    of  natural   theology   how   wonder- 


THE    ARGUMENT    FROM    SKILL.  21 

fully  do  we  find  that  it  has  borne  the  tests  both  of 
universality  and  of  experience.  Not  only  is  it  an  in- 
duction which  omits  no  known  fact,  but  it  is  an  induc- 
tion of  all  people,  in  all  ages,  and  under  all  conditions. 
How  unmoved  also  has  it  borne  the  test  of  experi- 
ence. Every  attempt  has  been  made  to  set  it  aside 
by  showing  how  this  universe  might  have  issued 
without  an  intelligent  Creator,  —  from  the  time  of 
the  "  fortuitous  concourse  of  atoms  "  of  Lucretius 
to  the  "  struggle  for  life  "  of  Darwin.  But  although 
by  stimulating  thought  and  inciting  deeper  study 
these  attempts  have  profoundly  modified  and  en- 
larged man's  earlier  crude  conceptions  of  the  Divine 
methods,  they  have  always  resulted  at  last  in  impress- 
ing the  great  mass  of  thinking  men  with  a  deeper  con- 
viction of  His  being,  with  a  grander  conception  of  His 
power,  and  with  a  more  profound  reverence  for  His 
skill,  who  is  the  Alpha  and  Omega  of  all  knowledge, 
the  Beginning  and  End  of  all  life. 

Beauty  is  simply  that  harmony  of  proportions  and 
qualities  which  results  from  the  most  complete  fitness 
of  all  the  parts  in  a  perfect  whole ;  and  in  the  educa- 
tion of  mankind  the  worship  of  skill  naturally  grew 
into  the  worship  of  beauty,  or  rather  of  that  material 
perfection  which  is  manifested  in  beauty.  Early  in  the 
history  of  civilization  the  culture  of  beauty  reached 
its  highest  development  in  ancient  Greece ;  and  then 
appeared  another  phase  of  the  argument  of  natural 
theology,  which,  for  the  sake  of  distinguishing  the 
stages  in  the  development  of  the  subject,  we  may  call 
the  argument  from  beauty,  although  it  does  not  differ 
essentially  from  the  argument  from  design.    As  before, 


22  THE   ARGUMENT   FROM   BEAUTY. 

the  argument  is  solely  an  induction.  We  have  for 
the  premises  the  infinite  beauty  of  nature,  and  for  the 
induction  the  inference  that  all  this  beauty  must  have 
issued  from  a  Personal  Being  vastly  more  susceptible 
than  any  human  nature  to  the  harmonies  of  form,  of 
color,  and  of  sound. 

This  argument,  although  not  recognized  as  such, 
has  a  singular  attraction  to  a  well  marked  class  in 
modern  society,  who,  having  revolted  from  the  pre- 
vailing creeds,  seek  satisfaction  for  their  minds  and 
hearts  in  the  contemplation  of  all  that  is  most  perfect 
in  art;  and  this  argument  strongly  appeals  to  a  vivid 
imagination  and  a  cultivated  taste.  These  worship- 
pers of  the  beautiful  hold  in  highest  honor  the  pro- 
ducts of  Greek  art  which  have  come  down  to  us,  and 
often  even  look  back  with  regret  to  that  old  civiliza- 
tion as  the  highest  stage  ever  reached  in  the  intellec- 
tual development  of  man.  But  Greek  beauty  was 
simply  a  material  beauty,  and  the  God  which  the 
Greek  apprehended  was  simply  a  perfect  sensuous 
being,  capable  of  realizing  in  his  person  and  his  cre- 
ation the  most  perfect  harmonies,  but  also  revelling 
in  the  sensuality  with  which,  before  Christianity,  ma- 
terial beauty  was  always  associated.  Lifted  into  a 
more  spiritual  sphere,  and  protected  by  the  safe- 
guards of  Christian  morality,  the  modern  devotees  of 
art  may  disassociate  material  beauty  from  such  gross 
accompaniments;  but  who  that  has  known  human 
nature  in  its  lower  moods  can  for  a  moment  question 
that  the  vilest  orgies  would  again  become  rife  if  the 
religious  convictions  by  which  alone  our  Christian 
civilization  is  maintained  were  undermined? 


THE   ARGUMENT   FROM   LAW.  23 

As  the  Greek  passed  under  the  Roman  sway,  so 
did  the  supremacy  of  beauty  yield  to  the  supremacy 
of  law;  and  this  was  a  natural  and  an  intellectual  pro- 
gress. Beauty,  as  we  have  seen,  is  the  harmony  of 
relations  which  perfect  fitness  produces ;  but  law  is 
the  prevailing  principle  which  underlies  that  har- 
mony, and  without  which  no  harmony  can  be  main- 
tained. In  the  ancient  world  Greece  appeared  as  the 
representative  of  beauty,  and  Rome  succeeded  as 
the  expositor  of  law.  In  the  fluctuations  of  nature 
the  material  forms  of  beauty  are  transient,  and  unless 
constantly  reproduced  under  the  operations  of  per- 
manent laws  can  have  no  lasting  influence.  In  Greece 
the  productiveness  of  art  soon  ceased,  through  failure 
of  the  authority  of  law  to  restrain  her  civil  dissen- 
sions, and  the  power  of  beauty  to  mould  men  lay 
dormant  until  Christianity  had  wrought  its  work,  and 
the  genius  of  beauty  became  wedded  to  the  spirit  of 
the  new  religion.  On  the  other  hand,  the  fundamental 
principles  of  law  are  eternal,  and  Rome,  through  her 
civil  law,  has  never  ceased  to  rule  the  world. 

It  was  a  very  long  step  in  the  progress  of  mankind 
from  the  promulgation  of  the  civil  law  of  Rome  to 
the  recognition  of  the  laws  of  nature, —  from  Justinian 
to  Newton ;  and  since  the  discovery  of  the  law  of 
gravitation  so  slowly  has  this  conception  pervaded 
the  popular  mind  that  not  until  our  own  day  have 
even  cultivated  men  fully  realized  that  their  race  has 
been  educated  under  a  reign  of  law,  which  embraces 
the  universe,  and  which  began  with  time, —  a  system 
of  laws  of  which  the  best  of  human  codes  offers  only 
a  feeble  type. 
3 


24    THE  ARGUMENT  OF  NATURAL  THEOLOGY. 

The  study  of  natural  laws  has  brought  fresh  evi- 
dence to  the  support  of  the  conclusions  of  natural 
theology,  and  evidence  of  the  most  impressive  kind. 
These  laws  are  at  once  so  grand  and  yet  so  simple, 
so  high  and  yet  so  near,  so  universal  and  yet  so  par- 
ticular, so  far  reaching  and  yet  so  present,  so  invari- 
able and  yet  so  beneficent,  that  while  they  tax  to  the 
utmost  his  intellectual  power,  they  are  calculated  to 
impress  the  mind  of  the  student  with  awe,  with  rever- 
ence, and  with  trust.  Newton  has  described  the  im- 
pression which  the  discovery  of  the  law  of  gravitation 
made  on  him,  and  many  of  the  great  masters  of 
science  join  to  his  their  united  testimony  that  the 
study  of  the  laws  of  nature  has  wrought  the  most 
profound  conviction  of  the  presence  of  an  overruling 
Mind.  The  devout  student  of  science  finds  it  difficult 
to  conceive  how  it  could  be  otherwise,  and  simply 
wonders  at  the  perversion  of  the  intellectual  vision  to 
which  the  heaviness  of  the  flesh  or  the  subtleties  of 
the  brain  may  sometimes  lead. 

The  phase  of  the  argument  of  natural  theology 
which  is  based  on  the  laws  of  nature,  we  have  called 
in  another  place  the  argument  from  general  plan; 
although,  like  the  argument  from  beauty,  it  is  not 
essentially  different  from  the  argument  from  design. 
The  writer  to  whom  we  have  before  referred  regards 
the  argument  from  general  plan  as  the  only  legiti- 
mate form  of  the  argument  from  design,  and  urges 
that  while  we  cannot  prove  that  fitness  may  not  have 
resulted  from  natural  selection,  or  from  some  other 
undefined  principle  of  nature,  order  must  always  be  a 
product  of  intelligence.    But,  obviously,  —  as  long  ago 


LAW   IMPLIES   A   LAWGIVER.  25 

Spinoza  so  powerfully  argued,  —  order,  or  law,  may- 
be merely  a  subjective  attitude  or  posture  of  our  own 
minds  towards  external  nature ;  and  the  words  "  law," 
"order,"  "plan,"  imply  personal  intelligence  as  plainly 
as  do  the  words  "design,"  "contrivance"  and  "adapta- 
tion" before  discussed.  To  say  that  law  implies  a  law- 
giver is  just  as  much  a  begging  of  the  question  as  to 
say  that  design  implies  a  designer.  The  truth  simply  is 
that  this  last  phase  of  the  argument  of  natural  theol- 
ogy, like  all  the  other  phases,  is  an  induction,  and  not  a 
necessary  deduction.  Of  this  induction  the  premises 
are  the  invariable  relations  of  natural  phenomena; 
and  the  inference  is  that  these  fixed  relations  must 
have  been  determined  by  a  Supreme  Intelligence, 
who  ordained  the  order  and  law  of  which  the  universe 
is  the  expression.  Christian  students  are  most  firmly 
persuaded  that  this  conclusion  is  the  only  reasonable 
or  intelligible  explanation  of  the  facts,  and  the  wider 
our  knowledge  becomes,  the  more  fully  is  their  con- 
viction confirmed.  But  it  is  easy  to  cavil,  —  that 
the  observed  constancy  of  relations  may  have  been 
caused  by  some  undefinable  potency  of  material 
things  (the  law  of  philotaxis,  for  example,  resulting 
from  a  tendency  in  the  leaves  of  a  plant  to  expose 
the  most  surface  to  the  sun),  and  then  the  whole 
matter  is  summed  up  with  the  scoffing  remark  of 
Voltaire,  "  The  heavens  only  declare  the  glory  of  the 
astronomers,"  who  see  their  own  intelligence  reflected 
in  the  circling  orbs.  If  we  would  protect  our  sacred 
cause  from  such  sneers,  we  must  be  careful  to  estab- 
lish it  in  truth,  and  not  claim  for  it  a  sanction  which 
it  does  not,  and  never  can  possess. 


26       THE  ARGUMENT   OF  NATURAL  THEOLOGY. 

We  have  now  passed  in  rapid  review  four  phases 
of  the  argument  of  natural  theology,  corresponding 
to  four  stages  in  human  development,  —  namely,  the 
argument  from  might,  the  argument  from  design,  the 
argument  from  beauty,  and  the  argument  from  gen- 
eral plan.  Corresponding  to  the  recognition  in  na- 
ture of  energy,  fitness,  beauty,  and  order,  we  have 
the  inferences  that  might,  skill,  perfection,  and  law 
are  the  attributes  of  an  Intelligence  which  created 
and  sustains  the  whole.  Here  the  scheme  of  natural 
theology  ordinarily  ends ;  but,  as  it  seems  to  us,  the 
culminating  phase  of  the  argument,  corresponding  to 
the  highest  phase  of  human  development,  still  re- 
mains to  be  stated. 

The  doctrines  of  Christianity  as  a  system  of  re- 
vealed religion  do  not  of  course  come  under  our 
consideration  ;  but  the  facts  of  Christianity  as  histor- 
ical verities  are  as  much  subjects  of  natural  theology 
as  any  other  natural  phenomena.  The  movements 
of  history  are  phenomena  of  nature  as  well  as  the 
movements  of  the  planets ;  and  considering  the  ad- 
mitted facts  of  our  holy  religion  from  this  point  of 
view,  what  a  broad  basis  for  induction  do  they  fur- 
nish !  Indeed,  the  basis  is  so  ample  that  we  may  at 
once  waive  everything  that  any  sceptic  will  question. 
We  may  admit  that  all  the  miraculous  features  of  the 
narrative  are  myths,  and  that  the  Bible  has  no  more 
authority  than  the  plays  of  Shakspeare,  or  any  other 
book  that  portrays  character.  Still,  after  all  conces- 
sions, there  remains  the  character  of  Jesus,  the  reve- 
lation of  perfect  holiness,  the  exemplar  of  the  noblest 
self-sacrifice,  the   manifestation  of  the    purest  love. 


THE  ARGUMENT  AN  INDUCTION.        2"] 

Admit  that  the  same  traits  have  in  some  degree 
appeared  in  the  founders  of  other  religions,  and  even 
in  classical  literature,  as  they  have  in  thousands  of 
humble  Christian  lives  ever  since.  Still,  there  re- 
mains the  wonderful  fact  that  this  one  character 
has  transformed  the  world,  and  led  to  incompar- 
ably the  highest  and  the  purest  civilization  which 
the  race  has  known.  From  these  premises  there  never 
has  been  but  one  inference  which  has  satisfied  the 
mass  of  mankind  who  have  come  to  the  full  knowl- 
edge of  the  facts,  —  the  conclusion  of  that  great  apostle 
who,  himself  overpowered  by  the  force  of  the  evi- 
dence, declared  that  "  God  was  in  Christ  reconciling 
the  world  unto  himself." 

Here  as  in  every  other  previous  phase  of  our  argu- 
ment we  have  simply  an  induction ;  not  a  demonstra- 
tion, but  an  induction  which  has  produced  conviction 
in  a  multitude  which  no  man  can  number;  which  has 
satisfied  the  deepest  yearnings  of  humanity;  which 
has  given  superhuman  courage  to  martyrs,  and  sus- 
tained the  unwavering  devotion  of  saints.  It  is  an 
induction,  moreover,  which  has  always  stood  the  test 
of  experience  under  every  circumstance  of  life ;  and 
among  its  confessors  have  been  all  sorts  and  condi- 
tions of  men,  from  the  humblest  intellect  to  the  most 
gifted  genius.  It  is  never  outgrown,  but  its  power 
increases  as  men  grow  in  wisdom  and  in  virtue.  It 
is  an  induction  which  opens  ever  fresh  fields  of  spir- 
itual knowlege,  and  directs  in  the  way  of  truth.  In 
a  word,  as  it  is  the  noblest  induction  that  man  has 
ever  grasped,  it  is  also  the  greatest  power  in  the 
world. 


28  THE  ARGUMENT  FROM  LOVE. 

We  thus  lay  hold  of  the  last  phase  of  the  argument 
of  natural  theology;  and  this  we  may  call  the  argu- 
ment from  love.  At  the  same  time  we  reach  the 
highest  stage  in  the  development  of  man's  concep- 
tion of  God.  How  gradual  but  how  majestic  has 
been  the  progress  in  the  education  of  mankind  from 
the  first!  How  large  the  result !  In  nature  man  found 
Energy,  Fitness,  Beauty,  Order,  and  Sacrifice;  and 
through  these  he  has  been  led  to  recognize  Might, 
Skill,  Perfection,  Law,  and  Love,  in  a  Supreme  Intelli- 
gence. The  argument,  however  its  materials  may 
differ,  is  in  spirit  one  throughout  all  its  varied  phases; 
and  the  one  point  we  would  impress  is  that  this  argu- 
ment is  an  induction.  To  show  the  validity  of  the 
argument  by  comparing  the  inductions  of  natural 
theology  with  the  inductions  of  science  will  be  the 
object  of  these  lectures. 


INDUCTION   AS   DEFINED   BY  ARISTOTLE.  29 


LECTURE    II. 

PREPARING   THE   WAY. 

IN  the  first  lecture,  when  drawing  the  distinction 
between  inductive  cognition  and  deductive  dem- 
onstration, we  used  the  word  "  induction  "  in  the  fa- 
miliar sense  in  which  it  is  usually  employed  among 
physicists,  to  include  the  numerous  phases  of  the 
experimental  method  of  discovering  general  truths, 
without  overlooking  the  fact  that  the  logicians  have 
generally  given  to  the  same  term  a  more  precise  and 
definite  meaning.  In  its  Greek  form  the  word  "  induc- 
tion "  is  as  old  as  Aristotle,  who  gives  a  formal  anal- 
ysis of  this  mode  of  reasoning,  which  is  not  more 
obscure  than  a  similar  philosophical  analysis  of  so 
complex  a  mental  process  might  be  at  the  present 
day. 

Certainly  the  great  Stagirite  had  grasped  the  essen- 
tial distinction  between  induction  and  deduction  when 
he  wrote :  "  Induction  makes  clear  only,  and  does 
not  prove."  And  although  he  confuses  his  modern 
reader  when  he  discusses  induction  as  a  proof  which 
may  be  formulated  in  a  syllogism,  he  elsewhere 
clearly  recognizes  this  mode  of  reasoning  as  a  kind 
of  inference  through  which  we  arrive  at  general  prin- 


30  INDUCTION  AS   DEFINED   BY   BACON. 

ciples.     A  more  precise  definition  of  the  mental  part 
of  the  process  could  not  now  be  given. 

Bacon,  who  is  regarded  by  English  scholars  as  the 
father  of  the  inductive  method,  held  a  more  mechan- 
ical view  of  the  subject.  In  nature  general  truths  are 
constantly  obscured  through  the  complexity  of  the 
data  furnished  by  experience ;  and  Bacon  proposed 
to  sift  them  out,  as  it  were,  by  a  perfectly  definite 
method  of  exclusion  or  elimination.  We  seek  the 
cause  of  a  certain  class  of  effects ;  say,  for  example, 
of  motion  in  circular  orbits.  Bacon  would  make  a 
critical  comparison  of  all  cases  in  which  the  effect  is 
produced  until  by  exclusion  of  one  after  another  of 
the  various  circumstances  he  is  able  to  detect  some 
phenomenon  constantly  present  when  the  effect  is 
present,  and  varying  in  degree  with  the  effect,  and 
without  which  the  effect  is  never  produced;  when 
this  phenomenon  —  if  one  lived  long  enough  to 
distinguish  it — must  be  a  cause  of  the  effect  in 
question.  Obviously,  an  exhaustive  elimination  of 
conditions  is  rarely  possible;  and  this  Bacon  recog- 
nizes, and  gives  rules  for  procedure  in  various  cases 
and  recommends  various  aids  to  induction,  —  "  ad- 
mincula  "  as  he  calls  them,  —  by  which  the  process 
may  be  greatly  expedited. 

Bacon's  method  was  the  normal  outcome  of  his 
metaphysics,  —  that  is,  of  his  a  priori  conception  of 
nature  and  of  natural  processes,  —  and  as  the  con- 
ception was  very  partial  the  method  was  necessarily, 
even  in  theory,  equally  limited.  Practically  no  great 
originator  in  science  ever  followed  Bacon's  rules,  or 
any  other  rules;    although  under  the  circumscribed 


bacon's  influence.  31 

conditions  of  ordinary  experimental  work  every  phys- 
ical investigator  naturally  resorts  to  a  method  of 
elimination  in  seeking  the  cause  of  any  accidental 
disturbance,  such  as  a  leak  in  his  apparatus,  or  a 
break  in  his  electrical  connections. 

It  is  a  singular  fact  that  Bacon,  who  is  usually  re- 
garded among  English-speaking  people  as  the  cham- 
pion who  freed  the  human  mind  from  servitude  to  a 
priori  dogmas,  should  himself  have  been  so  greatly 
influenced  by  his  metaphysics.  Bacon  constantly  set 
induction  in  opposition  to  deduction,  and  regarded 
syllogism  as  of  service  only  for  the  communication  of 
knowledge.  But,  obviously,  wherever  the  universal 
can  be  connected  with  the  particular  the  process  of 
thought  can  be  expressed  in  a  syllogism ;  and  if 
Bacon  could  have  succeeded  in  realizing  his  meta- 
physical conception  he  would  have  also  succeeded 
in  placing  induction  on  the  same  basis  as  deduction, 
and  rendered  the  method  equally  demonstrative. 

It  is  also  a  current  opinion  that  Bacon  was  the  first 
to  make  the  results  of  observation  and  experiment 
essential  factors  in  scientific  reasoning.  But  this, 
again,  is  only  partially  true.  Aristotle  constantly 
appealed  to  the  facts  of  nature  in  support  of  his  con- 
clusions, and  there  are  at  least  hints  in  his  writings  of 
experimental  methods;  and  in  classical  writings  of 
a  later  date  we  have  abundant  evidence  of  accurate, 
discriminating,  and  intelligent  observations.  As  com- 
pared with  Aristotle,  the  greater  influence  of  Bacon 
on  the  advancement  of  knowledge  is  not  to  be  found 
so  much  in  the  superiority  of  his  methods  as  in  the 
larger  knowledge  of  nature  and  the  clearer  scientific 


32  BACON   DID   NOT   INVENT   "  INDUCTION." 

conceptions  among  the  men  whom  he  influenced ; 
and  it  is  safe  to  say  that  if  the  "  Novum  Organum  " 
had  been  given  to  the  world  a  few  centuries  earlier 
it  would  have  led  to  no  greater  results  than  those 
produced  by  the  far  older  "  Organon "  which  it 
superseded. 

One  influence  of  Bacon's  great  genius  has  been  to 
spread  very  widely  the  narrow  meaning  which  he  ap- 
propriated for  the  word  "  induction."  Indeed,  accord- 
ing to  a  common  popular  misapprehension,  Bacon 
invented  the  word,  as  well  as  the  mechanical  method 
which  it  is  often  used  to  indicate.  But,  as  has  been 
intimated,  this  word,  or  its  equivalent  in  different 
languages,  has  been  in  constant  use  from  the  time  of 
Aristotle ;  and  was  employed  by  the  Stagirite  with  a 
far  more  comprehensive  and  deeper  meaning  than 
was  ever  conceived  by  King  James's  at  once  great 
and  contemptible  chancellor.  We  now  use  the  term 
in  a  far  broader  sense  than  ever  before ;  but  so  far  as 
the  preliminary  mental  act  is  concerned,  our  concep- 
tion of  the  process  of  induction  does  not  differ  ma- 
terially from  that  of  Aristotle.  Its  essential  features 
are,  first,  the  conception  or  guess  ;  secondly,  the 
verification  of  this  conception  by  experiment  and 
observation.  The  verification  may  be  direct,  or 
through  some  more  or  less  remote  deduction ;  and  if 
the  appeal  to  nature  shows  that  the  first  conception 
must  be  rejected,  the  experience  will  probably  sug- 
gest some  modification  which  will  be  tested  in  like 
manner  in  its  turn,  until  the  truth  in  more  or  less 
completeness  is  reached. 

This  system  of  observation   and  experiment,  con- 


BASIS   OF  SUCCESSFUL  INDUCTION.  33 

tinued  during  a  long  period  of  time,  has  given  to  the 
modern  world  a  far  more  intimate  acquaintance  with 
natural  phenomena  than  the  ancients  possessed  ;  and 
it  is  to  this,  and  not  to  superior  philosophy,  that  our 
great  success  in  the  advancement  of  knowledge  is 
to  be  attributed. 

You  pronounce  with  confidence  on  the  probability 
of  a  friend's  action  in  a  given  case  in  measure  as  you 
are  acquainted  with  his  principles  and  inclinations. 
In  a  very  similar  way  the  investigator  who  is  ac- 
quainted with  nature  and  her  processes  is  likely  to 
make  inferences,  which  will  be  confirmed  by  experi- 
ence in  just  the  proportion  that  his  knowledge  is 
wider  and  more  exact.  The  ancients  were  often  as 
ingenious  and  as  profound  in  their  conceptions 
as  modern  philosophers,  and  their  anticipations  of 
knowledge  surprise  us.  But  as  their  conceptions 
remained  unverified,  they  laid  no  sure  foundations 
on  which  they  could  build.  Because  wild  and  scat- 
tered, all  their  ingenuity  was  misdirected  and  unavail- 
ing. The  value  of  a  man's  guess  depended  on  his 
reputation ;  and  questions  of  fact  were  settled  on 
authority.  Thus  it  came  to  pass  that  Aristotle's 
unverified  conjectures,  through  the  sheer  force  of  his 
intellectual  pre-eminence,  misled  the  world  for  two 
thousand  years. 

Besides  his  more  intimate  acquaintance  with  na- 
ture, the  modern  student  is  constantly  acquiring  im- 
proved methods  of  testing  his  inferences ;  and  such 
instruments  as  the  telescope,  the  microscope,  the 
polariscope,  the  spectroscope,  the  thermometer,  the 
galvanometer,  and  the  telephone  have  not  only  im- 


34  PREPARING  THE  WAY. 

mensely  widened  his  field  of  observation,  but  also 
vastly  increased  his  power  of  experimenting ;  so  that 
his  progress  in  knowledge  has  been  so  constantly 
and  so  rapidly  accelerated  that  more  has  been 
gained  during  the  lifetime  of  men  still  living  than 
during  all  human  history  before. 

As  our  object  in  these  lectures  is  to  show  that  the 
inductions  of  natural  theology  are  as  legitimate  as  the 
inductions  of  physical  science,  it  is  essential  that  we 
should  first  describe  the  characteristics  of  scientific 
inductions,  in  the  broad  sense  with  which  we  use  this 
term ;  and  since,  as  we  have  endeavored  to  show,  it 
is  impossible  to  define  this  mode  of  reasoning  by  any 
concise  formula,  we  shall  best  attain  our  object  by 
studying  a  few  striking  examples,  —  selecting  for  ex- 
amination great  discoveries  whose  history  is  well 
known,  and  of  which  the  important  steps  can  readily 
be  traced.  Let  us  begin,  however,  with  a  brief  de- 
scription of  some  of  the  speculations  of  the  old 
Greek  philosophers,  in  order  that  by  comparison  we 
may  more  fully  appreciate  the  value  of  our  modern 
inductive  methods. 

It  will  be  remembered  that  the  Father  of  History, 
when  seeking  to  explain  the  cause  of  the  annual  in- 
undations of  the  Nile, — after  giving  his  reasons  with 
a  truly  scientific  spirit  (if  sometimes  with  insufficient 
knowledge)  for  rejecting  the  hypotheses  which  had 
been  proposed  to  him,  —  proceeds  to  argue  that  the 
effect  is  caused  by  the  sun,  which  unequally  draws 
the  water  from  the  sources  of  the  stream  at  different 
seasons  of  the  year ;  and  that  the  overflow  takes 
place  when  the  sun  has  gone  north,  and  draws  less 


ILLUSTRATION   FROM   HERODOTUS.  35 

powerfully  on  the  Libyan  fountains,  which  then  pour 
out  their  full  supply. 

Assuming  the  sufficiency  of  the  alleged  cause,  the 
explanation  of  Herodotus  is  still  confused;  but  what, 
as  it  seems  to  me,  he  distinctly  implies  is  this :  The 
Nile  is  unique  among  rivers,  first,  because  it  flows 
from  the  south  to  the  north,  across  the  region  twice 
traversed  by  the  sun  in  the  course  of  the  seasons ; 
and  secondly,  because,  having  no  tributaries,  it  is  not 
affected  by  the  rains  along  its  banks.  Hence  the 
alternations  of  its  floods  must  depend  on  its  sources 
alone ;  and  the  sun-god  must  produce  the  greatest 
possible  difference  of  effect  on  these  springs  when 
at  the  extreme  limits  of  his  annual  journey. 

Were  the  cause  adequate  this  explanation  certainly 
would  not  be  unphilosophical;  but  all  turns  on  this 
one  point.  Herodotus  does  not  appear  to  have  had 
any  doubts  about  the  adequacy  of  the  sun's  agency, 
or  to  have  made  any  attempts  to  estimate  the  magni- 
tude of  the  effect  which  could  thus  be  produced. 
His  whole  theory  was  expressed  by  the  phrase,  "he 
(the  sun)  draws  the  water  to  him,"  —  a  form  of 
words  which  has  been  used  to  describe  a  certain  fa-, 
miliar  appearance  in  the  heavens  from  that  day  until 
this.  In  using  this  expression  —  with  which  his  read- 
ers at  once  associated  the  optical  phenomenon  just 
referred  to,  and  which  they  connected  in  an  obscure 
way  with  the  evaporation  of  water  —  Herodotus  felt 
that  he  was  giving  a  triumphant  explanation ;  and 
this  example  shows  in  a  marked  way  the  reason  of 
the  unsoundness  of  the  Greek  philosophy  when 
applied  to  the  study  of  nature.     The  old  Greeks  had 


36  PREPARING  THE   WAY. 

as  vivid  imaginations,  and  were  as  acute  reasoners  as 
ourselves ;  they  were  also  in  many  cases  diligent 
and  careful  observers.  But  they  mistook  abstract  con- 
ceptions for  realities ;  and  having  given  names  to 
these  forms  of  thought,  they  sought  to  advance 
knowledge  by  analyzing  the  words  and  the  thoughts 
suggested,  instead  of  studying  the  facts  which  the 
words  signify. 

This  vicious  method  of  Greek  philosophy  is  well 
described  by  Whewell  in  his  "  History  of  the  Induc- 
tive Sciences :  "  "  As  soon  as  they  had  introduced 
into  their  philosophy  any  abstract  and  general  con- 
ceptions, they  proceeded  to  scrutinize  these  by  the 
internal  light  of  the  mind  alone,  without  any  longer 
looking  abroad  into  the  world  of  sense.  They  took 
for  granted  that  philosophy  must  result  from  the  re- 
lations of  those  notions  which  are  involved  in  the 
common  use  of  language,  and  they  proceeded  to 
seek  their  philosophical  doctrines  by  studying  such 
notions.  They  ought  to  have  reformed  and  fixed 
their  usual  conceptions  by  observation ;  they  only 
analyzed  and  expanded  them  by  reflection.  They 
ought  to  have  sought  by  trial,  among  the  notions 
which  passed  through  their  minds,  some  one  which 
admitted  of  exact  application  to  facts ;  they  selected 
arbitrarily,  and  consequently  erroneously,  the  notions 
according  to  which  facts  should  be  assembled  and 
arranged.  They  ought  to  have  collected  clear  fun- 
damental ideas  from  the  world  of  things  by  induc- 
tive acts  of  thought;  they  only  derived  results  by 
deduction  from  one  or  other  of  their  familiar 
conceptions." 


SLAVERY  TO    LANGUAGE.  37 

But  although  the  false  method,  thus  so  clearly  de- 
scribed, was  especially  characteristic  of  the  ancient 
philosophy,  it  is  a  vice  from  which  the  modern  world 
has  by  no  means  wholly  escaped.  How  often  do  the 
controversies  of  the  present  day  turn  on  purely  ver- 
bal distinctions.  How  imperiously,  and  yet  often  how 
insensibly,  are  our  thoughts  ruled  by  the  mysterious 
mechanism  of  language.  How  conscious  is  the  effort 
to  force  language  to  express  our  exact  and  deliberate 
thought,  and  to  prevent  our  thought  from  being 
moulded  by  language.  Of  course  to  a  very  large 
extent  the  influence  of  language  is  legitimate.  Lan- 
guage is  the  medium  of  thought,  and  cannot  be  sep- 
arated from  it.  Exact  thought  is  not  practicable 
without  language,  and  the  very  effort  to  clothe  thought 
in  words  awakens  thought.  Moreover,  the  general 
terms  in  language  represent  stages  of  intellectual 
progress.  They  form  a  scaffolding,  as  it  were,  by 
which  the  mind  mounts  to  ever  higher  levels  from 
which  it  gains  a  more  general  and  wider  prospect. 
But  it  is  one  thing  to  use  language,  and  another  thing 
to  be  a  slave  to  it.  Some  men  are  slaves  to  language 
all  their  lives,  and  from  such  a  slavery  the  ancient 
philosophy  was  not  liberated  until  modern  times. 

Man  was  made  in  the  image  of  his  Maker;  or,  to 
express  the  same  truth  in  the  phraseology  of  a  re- 
cent philosophy,  has  developed  into  harmony  with 
his  environment;  and,  undoubtedly  for  this  reason, 
those  acute  thinkers  of  ancient  time  in  their  unveri- 
fied conceptions  not  unfrequently  anticipated  the 
results  of  modern  science.  So  it  was  with  Herodo- 
tus ;   and,  although  he  attached  no  definite  meaning 


38  PREPARING  THE   WAY. 

to  it,  his  explanation  of  the  annual  overflow  of  the 
Nile  was  in  the  main  correct.  The  sun  is  indeed  the 
cause ;  and  the  great  pump  which  the  sun  maintains 
in  ceaseless  action  not  only  supplies  the  Nile,  but 
also  all  the  rivers  of  the  globe.  Moreover,  such  is 
the  peculiar  equatorial  position  of  the  basin  of  drain- 
age of  this  remarkable  river  that  the  evaporation 
from  this  area  greatly  diminishes  as  the  sun  moves 
north  of  the  equator,  when  naturally  an  increased 
amount  of  water  flows  down  the  only  other  outlet. 

By  the  Greek  philosophers  the  contrasts  empha- 
sized by  language  were  regarded  as  fundamental  dis- 
tinctions in  nature,  or  first  principles,  which  they 
made  the  basis  of  discussion,  and  from  which  they 
sought  to  deduce  general  truths.  Aristotle  enumer- 
ates ten  such  principles,  as  based  by  the  Pythag- 
oreans on  the  contrasts  of  number:  limited  and 
unlimited,  odd  and  even,  one  and  many,  right  and 
left,  male  and  female,  rest  and  motion,  straight 
and  curved,  light  and  darkness,  good  and  evil,  square 
and  oblong;  and  from  oppositions  of  this  kind  Aris- 
totle himself  deduced  the  doctrine  of  the  four 
elements. 

"  We  seek,"  he  says,1  "  the  principles  of  sensible 
things,  —  that  is,  of  tangible  bodies.  We  must  take, 
therefore,  not  all  the  contrarieties  of  quality,  but 
those  only  which  have  reference  to  the  touch.  Thus 
black  and  white,  sweet  and  bitter,  do  not   differ  as 

1  As  translated  from  De  Gen.  et  Corrupt.  :  Whewell's  His- 
tory of  the  Inductive  Sciences,  vol.  i.  page  49,  edition  of  1847  ; 
and  the  translations  from  Aristotle  which  follow  are  quoted 
from  the  same  standard  work. 


DOCTRINE   OF  THE   FOUR  ELEMENTS.  39 

tangible  qualities,  and  therefore  must  be  rejected  from 
our  consideration.  Now  the  contrarieties  of  quality 
which  refer  to  the  touch  are  these :  hot,  cold ;  dry, 
wet;  heavy,  light;  hard,  soft;  unctuous,  meagre; 
rough,  smooth ;  dense,  rare."  Then,  after  rejecting 
all  but  the  first  four  of  these,  either  because  they 
are  not  active  and  passive  qualities,  or  because  they 
are  combinations  of  the  four  first,  and  concluding  for 
these  reasons  that  the  four  retained  must  be  elements, 
he  proceeds : — 

"  Now  in  four  things  there  are  six  combinations  of 
two ;  but  the  combinations  of  two  opposites,  as  hot 
and  cold,  must  be  rejected.  We  have  therefore  four 
elementary  combinations  which  agree  with  the  four 
apparently  elementary  bodies ;  fire  is  hot  and  dry ; 
air  is  hot  and  wet  (for  steam  is  air) ;  water  is  cold 
and  wet;  earth  is  cold  and  dry." 

In  a  similar  way  by  considering  light  as  opposite 
to  heavy  Aristotle  came  to  regard  levity  as  a  quality 
of  a  body,  and  distinguished  bodies  as  absolutely 
heavy  or  absolutely  light.  "  Former  writers "  he 
says,  "have  considered  heavy  and  light  relatively 
only,  —  taking  cases  where  both  things  have  weight, 
but  one  is  lighter  than  the  other;  and  they  imagined 
that  in  this  way  they  defined  what  was  absolutely 
heavy  and  light."  Fire  and  air,  according  to  Aristotle, 
were  absolutely  light,  with  fire  the  lighter  of  the 
two.  Hence  it  followed  "  that  each  of  the  four  ele- 
ments tends  to  its  own  place,  —  fire  being  the  highest, 
air  the  next,  water  the  next,  and  earth  the  lowest." 
In  another  place  he  writes :  "  heavy  and  light  are,  as 
it  were,  the  embers  or  sparks  of  motion  ; "  and  he 
4 


40        SPECIFIC   GRAVITY  AND   SPECIFIC   LEVITY. 

considered  that  the  tendency  of  light  bodies  to  rise, 
like  the  tendency  of  heavy  bodies  to  fall,  was  an  in- 
herent quality. 

It  is  obvious  that  all  this  fallacious  reasoning  had  a 
purely  verbal  origin;  and  that  the  great  error  con- 
sisted in  inferring  that  there  must  be  an  opposition 
of  material  qualities  corresponding  to  verbal  distinc- 
tions. Since  light  was  opposite  to  heavy,  the  con- 
clusion was  drawn  that  levity,  like  weight,  must  be  a 
quality  of  matter;  and  it  was  nearly  two  thousand 
years  before  men  found  out  that  levity,  or  buoy- 
ancy,—  as  we  now  call  the  upward  tendency  of  tim- 
ber in  the  sea,  or  of  flame  and  other  forms  of  heated 
vapors  in  the  atmosphere,  —  the  phenomena  out  of 
which  the  Stagirite  made  so  much, —  was  simply  an 
effect  of  the  weight  of  a  surrounding  fluid ;  and  we 
retain  in  our  language  the  term  specific  gravity  — 
originally  opposed  to  specific  levity — as  a  constant 
reminder  of  the  persistency  of  error.  Moreover,  it  is 
a  striking  illustration  of  the  spirit  with  which  the  an- 
cient philosophy  was  cultivated,  that  this  error  pre- 
vailed in  spite  of  the  fact  that  Archimedes  discovered 
and  correctly  enunciated  the  simple  principle  of  buoy- 
ancy, —  a  discovery  rendered  most  notable  by  its  con- 
nection with  the  testing  of  King  Hiero's  crown. 

We  must  also  briefly  notice  Aristotle's  absurd  con- 
clusions in  regard  to  motion ;  since  they  were  gen- 
erally received  even  down  to  the  period  of  the  great 
astronomical  inductions  which  we  are  next  to  con- 
sider, and  without  some  knowledge  of  them  we  can- 
not comprehend  the  intellectual  conditions  under 
which  the   great   astronomers   of   the   sixteenth  and 


MOTION  AN  INHERENT  TENDENCY.      4 1 

seventeenth  centuries  studied  and  labored.  Motion, 
according  to  the  Stagirite,  was  simply  the  effect  of 
the  inherent  tendency  of  the  body.  In  consequence 
of  their  nature,  light  bodies  move  upwards  and  heavy 
bodies  downwards;  and,  as  was  fully  recognized, 
such  motions  acquire  an  ever  increasing  velocity. 
Since,  then,  acceleration  was  the  characteristic  of 
the  motion  of  a  body  obeying  its  natural  tendency, 
such  motions  were  regarded  as  natural.  On  the 
other  hand,  when  a  ball  is  rolled  along  the  ground 
the  motion  rapidly  diminishes,  and  finally  ceases, 
because  the  ball  is  forced  against  its  inherent  dis- 
position; and  hence,  on  the  principle  of  oppositions, 
such  retarded  motions  were  distinguished  as  violent. 

This  explanation,  if  it  may  be  so  called,  of  the 
motions  of  bodies  remained  almost  unquestioned  to 
the  time  of  Galileo ;  and  the  results  of  his  exper- 
iments were  gravely  questioned  because  they  were 
inconsistent  with  the  Aristotelian  dogmas.  But  the 
climax  of  these  unbridled  dynamical  speculations 
remains  yet  to  be  stated,  and  will  form  the  turning- 
point  in  this  discourse. 

In  his  book  "  On  the  Heavens"  Aristotle  wrote: 
"  The  simple  elements  must  have  simple  motions ; 
and  thus  fire  and  air  have  their  natural  motions 
upward,  and  water  and  earth  have  their  natural  mo- 
tions downward.  But  besides  these  motions  there 
is  motion  in  a  circle,  which  is  unnatural  to  these  ele- 
ments, but  which  is  a  more  perfect  motion  than  the 
other,  because  a  circle  is  a  perfect  line,  and  a  straight 
line  is  not;  and  there  must  be  something  to  which 
this  motion  is  natural.     From  this  it  is  evident  that 


42  THE   QUINTA   ESSENTIA. 

there  is  some  essence  of  body  different  from  those 
of  the  four  elements,  more  divine  than  those  and  su- 
perior to  them.  If  things  which  move  in  a  circle 
move  contrary  to  nature,  it  is  marvellous,  or  rather 
absurd,  that  this,  the  unnatural  motion,  should  alone 
be  continuous  and  eternal ;  for  unnatural  motions  de- 
cay speedily.  And  so  from  all  this  we  must  collect 
that  besides  the  four  elements  which  we  have  here 
and  about  us,  there  is  another  removed  far  off,  and 
the  more  excellent  in  proportion  as  it  is  more  dis- 
tant from  us."  This  fifth  element  was  called  the 
"  quinta  essentia "  by  Latin  writers ;  and  the  word 
"  quintessence  "  in  our  own  language  frequently  brings 
to  mind  this  singular  conception,  which,  although  so 
absurd  to  us,  held  for  ages  a  wonderful  control  over 
the  human  mind. 

Having  thus  shown  how  vain  and  foolish  are  the 
imaginations  of  men  unless  directed  and  controlled 
by  experience,  we  turn  next  with  satisfaction  to  a  far 
more  glorious  record,  and  shall  attempt  to  illustrate 
by  a  conspicuous  example  how  this  same  noble  and 
powerful  imagination  of  man  becomes  like  a  divine 
inspiration  if  only  he  approaches  nature  with  meek- 
ness, and  strives  to  learn  what  she  alone  can  teach. 
It  is  the  disposition  of  the  mind  and  the  fulness  of 
knowledge,  more  than  method,  more  than  skill,  more 
than  ingenuity,  more  than  intellect,  which  makes  the 
difference  between  foolish  speculation  and  pregnant 
conception. 

The  change  from  the  ancient  philosopher  to  the 
modern  investigator  is  as  great  as  the  difference 
between  the  sophist  and  the  scholar,  between  self- 


INFLUENCE   OF   CHRISTIANITY.  43 

assertion  and  self-devotion,  between  conceit  and  hu- 
mility, between  pretension  and  worship.  This  change 
of  attitude  of  the  students  of  nature  since  the  revival 
of  learning  is  often  ascribed  to  the  influence  of  Bacon. 
But  great  thinker  as  Bacon  was,  he  did  not  lead  the 
change,  and  knew  little  of  its  true  spirit.  To  explain 
such  a  wide-spread  intellectual  movement  we  must 
look  to  a  more  potent  cause  than  the  influence  of 
any  man,  however  great;  and,  as  it  seems  to  me,  this 
great  revolution  can  be  directly  traced  to  the  in- 
fluence of  Christianity,  and  to  the  spirit  of  humility 
and  self-devotion  which  its  Founder  sanctified  and 
rendered  glorious. 

The  Law  of  Universal  Gravitation,  says  Dr.  Whewell, 
the  historian  of  the  inductive  sciences1  "is  indisputa- 
bly and  incomparably  the  greatest  scientific  discov- 
ery ever  made,  whether  we  look  at  the  advance 
which  it  involved,  the  extent  of  the  truth  disclosed, 
or  the  fundamental  and  satisfactory  nature  of  this 
truth."  And  although  it  may  be  doubted  whether 
this  discovery  was  as  an  intellectual  achievement  any 
greater  than  many  others  which  have  been  made  since, 
there  can  be  no  question  that  not  one  of  these,  how- 
ever brilliant,  has  had  so  great  and  lasting  an  effect  in 
the  advancement  of  learning.  Selecting,  therefore, 
the  law  of  gravitation  as  a  most  conspicuous  example 
of  a  scientific  induction,  let  us  endeavor  to  follow,  as 
far  as  is  possible,  the  several  steps  by  which  the  great 
result  was  achieved,  in  order  that  we  may  thus  gain 
a  clearer  conception  of  the  mental  process,  called  in- 
duction, which  we  are  seeking  to  illustrate. 

1  Whewell's  History  of  the  Inductive  Sciences,  vol.  ii.  p.  187. 


44  PRELUDE  TO  NEWTON. 

In  order  to  understand  what  Newton  accomplished, 
it  is  essential  that  by  studying  the  state  of  knowledge 
at  his  time  we  should  put  ourselves  in  some  measure 
in  his  position  when,  at  the  age  of  twenty-three,  he 
received  the  degree  of  Bachelor  of  Arts  at  the  Uni- 
versity of  Cambridge.  Thorough  mathematical  stu- 
dent of  great  ability  that  he  was,  we  must  suppose 
him  versed  in  all  the  astronomical  learning  of  the 
day ;  but  at  the  same  time  he  must  have  been  more 
or  less  hampered  and  prejudiced  by  the  forms  and  doc- 
trines in  which  he  had  been  educated,  —  limitations 
from  which  only  men  of  genius  are  able  to  escape. 
On  the  other  hand  we  must  remember  that  besides 
the  astronomical  works  which  had  been  actually  pub- 
lished and  were  then  common  property,  Newton  also 
had  the  advantage  of  a  large  amount  of  floating  dis- 
cussion, which  did  not  ripen  into  definite  results  until 
a  later  day,  but  which  made  Newton's  grasp  of  the 
great  ideas  involved  in  his  discovery  a  more  natural 
and  less  transcendent  effort  than  it  would  otherwise 
appear. 

Such  historical  relations  as  we  would  establish  are, 
however,  very  difficult  to  secure ;  for  even  if  we  can 
fully  realize  the  conditions  of  actual  knowledge  in 
Newton's  time  we  cannot  appreciate  those  influences 
of  education,  surroundings,  and  other  circumstances 
which  so  greatly  modify  the  intellectual  atmosphere 
in  which  men  live  and  work,  and  by  which  facts  and 
opinions  are  always  more  or  less  colored.  Hence,  it 
is  impossible  for  any  one  at  the  present  day,  even 
after  long  continued  study  and  investigation,  to  stand 
where  Newton  stood  in  his  opening  manhood,  and 


THE    ALMAGEST.  45 


view  the  field  of  knowledge  as  he  saw  it ;  and  for  me 
it  is  only  practicable  to  sketch  the  situation  in  rudest 
outlines. 

The  knowledge  of  astronomical  facts  acquired  by 
the  ancients  was  very  extensive.  From  the  time  of 
the  Chaldean  shepherds  there  were  always  numerous 
and  assiduous  observers  of  celestial  phenomena.  In- 
deed, among  eastern  nations  the  heavenly  hosts  were 
so  universally  objects  of  worship,  and  the  conjunc- 
tions of  the  planets  were  supposed  to  be  so  intimately 
connected  with  men's  lives  that  astronomical  occur- 
rences received  an  attention  which  no  other  phe- 
nomena of  nature  secured.  As  early  as  150  B.C. 
Hipparchus  constructed  a  system  of  astronomy  which 
even  now  commands  our  admiration.  We  have  a 
very  full  exposition  of  this  system  by  Ptolemy,  who 
lived  under  the  Emperor  Hadrian  two  hundred  and 
fifty  years  later,  and  whose  work  has  been  preserved 
for  us  by  the  Arab  astronomers  under  the  title  of  "The 
Almagest."  Ptolemy  added  but  little  to  the  theory  of 
Hipparchus,  but  he  did  a  great  deal  to  extend  and 
verify  it.  "  The  Almagest"  is  a  monument  to  his  learn- 
ing, accuracy,  judgment,  and  skill;  and  is  by  far  the 
most  important  contribution  to  scientific  knowledge 
which  we  have  received  from  the  ancient  world. 

When  we  remember  that  the  observations  of  the 
ancients  were  made  with  no  aids,  or  with  only  the 
rudest  tools,  the  knowledge  of  celestial  phenomena 
which  had  been  acquired  at  the  time  of  Hippar- 
chus appears  wonderful.  The  fixity  of  the  stars  had 
been  established.  The  brighter  stars  had  not  only 
been  grouped  in  constellations  and  mapped,  but  their 


46  ASTRONOMY   OF  THE   ANCIENTS. 


relative  positions  had  been  determined,  by  alignments, 
with  such  accuracy  that  the  observations  arc  of  value 
at  the  present  day.  The  paths  of  the  planets  and  of 
the  moon  —  and  what  is  still  more  remarkable,  the 
course  of  the  sun  through  the  constellations  —  had 
been  followed,  and  the  varying  rapidity  of  their  mo- 
tions in  different  parts  of  their  sinuous,  and  often  in- 
voluted, courses  recorded.  Numerous  cycles  had 
been  discovered  which  enabled  the  astronomers  to 
regulate  the  calendar,  predict  eclipses,  and  foretell 
other  astronomical  conjunctions.  Some  of  these 
cycles,  like  the  cycle  of  Meton,  —  which  is  still  used 
for  calculating  the  time  of  Easter,  and  in  which  the 
Golden  Number  is  the  number  of  the  current  year, — 
are  so  extended  that  their  discovery  implies  the 
maintenance  of  observations  and  the  preservation  of 
the  records  through  long  periods  of  time.  In  addi- 
tion to  all  this  the  great  circles  of  the  celestial  sphere 
had  been  marked  out,  the  equinoctial  and  solstitial 
points  had  been  fixed,  and  Hipparchus  himself  had 
discovered  the  precession  of  the  equinoxes.  Lastly, 
the  spherical  form  of  the  earth  had  been  recognized, 
and  some  approach  had  been  made  to  a  knowledge 
of  its  dimensions. 

The  circumstance  that  the  vault  of  the  sky  forms  a 
sort  of  natural  map  on  which  the  paths  of  the  planets 
and  of  the  moon  can  be  directly  traced  by  the  un- 
aided eye,  and  that  of  the  sun  readily  inferred  from 
what  was  called  the  "  heliacal "  rising  and  setting  of 
known  stars,  in  connection  with  the  religious  impor- 
tance attached  to  the  subject,  was  undoubtedly  the 
reason  that   the  ancients  acquired   an  acquaintance 


THEIR   PRACTICAL   KNOWLEDGE.  47 

with  astronomical  facts  so  far  beyond  their  general 
knowledge  of  natural  phenomena;  and  it  is  not  to 
the  credit  of  our  modern  education  that  the  learned 
men  of  those  early  times  had  a  better  acquaintance 
with  the  changing  appearances  of  the  spangled  dome 
of  heaven  than  any  of  our  scholars  at  the  present 
day,  except  those  who  especially  devote  themselves 
to  astronomical  studies.  It  is  certainly  a  matter  of 
great  regret  that  our  methods  of  education  should 
not  invite  our  children  to  observe  what  is  going  on 
around  and  above  them.  With  the  help  of  diagrams 
and  orreries  they  learn  from  more  or  less  popular 
text-books  the  outlines  of  the  modern  system  of 
astronomy,  and  perhaps  gain  some  conception  of  the 
immensity  of  space  ;  but  they  remain  ignorant  of  the 
appearances  which  the  skies  unroll  every  clear  night 
before  their  eyes. 

When  looking  from  my  summer  home  towards  an 
uninterrupted  eastern  horizon  I  have  often  heard  in- 
telligent people  express  surprise  that  the  full-orbed 
moon  which  rose  from  the  waves  the  previous  night 
should  rise  behind  the  hills  the  next;  and  although 
this  maybe  an  unusual  experience,  I  question  whether 
many  of  the  graduates  of  our  colleges  have  a  clear 
conception  of  the  singular  involutes  which  the  plan- 
ets would  be  seen  to  follow  if  each  left  a  shining  track 
in  its  wake;  and  certainly  still  fewer  have  any  idea  of 
the  very  tortuous  course  of  the  moon  in  her  succes- 
sive lunations,  until  after  a  long  period  she  retraces 
very  nearly  the  same  course  again.  But  these  are 
the  very  phenomena  out  of  which  our  system  of  as- 
tronomy was  constructed;    and  if  we  would  under- 


48  COPERNICUS. 


stand  what  the  great  astronomers  did  we  must  first 
become  acquainted  with  the  appearances  whose  coils 
they  unwound  and  whose  complexity  they  unravelled. 
During  the  long  night  of  the  dark  ages  which  suc- 
ceeded the  fall  of  the  Roman  Empire,  the  records  of 
ancient  astronomy  were  preserved  at  Bagdad,  at  Cairo, 
and  at  Cordova,  those  centres  of  Moslem  culture. 
With  the  revival  of  learning  in  the  Christian  world, 
soon  after  the  capture  of  Cordova  by  Ferdinand  the 
Third,  of  Castile,  in  1236,  astronomy  became  a  favor- 
ite subject  of  study  throughout  Europe,  and  in  this 
study  the  "  Almagest  "  of  Ptolemy  was  the  great  au- 
thority ;  and  two  centuries  and  a  half  later,  just  at  the 
dawn  of  the  Reformation,  when  Ferdinand  and  Isa- 
bella were  raising  the  united  standards  of  Aragon  and 
Castile  on  the  last  stronghold  of  the  Moors  in  Spain, 
where  Columbus  was  present  seeking  from  their  Cath- 
olic Majesties  commission  and  supplies  for  his  first 
memorable  voyage,  there  was  at  the  University  of  Cra- 
cow in  Poland  a  young  student,  named  Nicholas  Co- 
pernicus, who  was  soon  to  become  the  greatest  master 
of  the  astronomical  knowledge  of  his  age.  After 
finishing  his  course  at  Cracow,  Copernicus  studied 
astronomy  first  at  Bologna,  then  at  Padua,  and  after- 
wards at  Rome  ;  but  having  gained  the  highest  honors 
at  these  great  seats  of  mediaeval  scholarship,  and  the 
reputation  of  being  the  most  learned  man  of  his  time, 
at  the  age  of  thirty  he  retired  to  the  little  town  of 
Frauenburg  in  eastern  Prussia,  where  he  spent  the  re- 
maining forty  years  of  his  life  as  a  tender  and  devoted 
pastor  of  a  rude  and  ignorant  flock.  To  Frauenburg 
Copernicus  had  carried  a  grand  conception,  and  in 


COPERNICUS.  49 


his  simple  lodgings,  still  shown  in  the  neighboring 
hamlet  of  Allenstein,  that  conception  was  matured. 

The  astronomy  of  which  Copernicus  was  so  great 
a  master  was  the  science  constructed  by  Hipparchus 
and  illustrated  by  Ptolemy,  and  which  had  remained 
essentially  unaltered  for  more  than  a  thousand  years. 
The  chief  merit  of  existing  treatises  was  the  wealth  of 
facts,  and  the  records  of  conscientious  observations 
which  they  contained ;  and  Copernicus  was  as  famil- 
iar with  the  dubious  ways  of  the  celestial  wanderers 
as  is  a  shepherd  with  the  by-paths  of  his  straying 
lambs.  His  knowledge,  moreover,  was  not  mere  eru- 
dition ;  but  the  facts  were  ever  present  with  him,  and 
the  paths  of  the  heavenly  bodies  were  engraved  as 
clearly  on  the  crystal  sphere  of  his  imagination  as  if 
on  the  firmament  they  were  marked  with  a  shining 
thread  among  the  stars. 

But  all  this  real  knowledge  came  to  Copernicus  in 
the  guise  of  a  system  which,  although  based  on  as- 
sumption, was  consecrated  by  authority  and  tradition, 
and  held  by  the  learned  world  with  the  same  rever- 
ence with  which  it  still  honors  the  models  of  clas- 
sical literature.  As  the  earth  was  regarded  as  the 
centre  of  the  universe,  and  the  circle  as  the  most 
perfect  of  figures,  the  astronomers  assumed  that  the 
heavenly  bodies  must  move  around  this  globe  in  cir- 
cular orbits.  But  as  the  involutions  of  the  planetary 
paths  were  obviously  inconsistent  with  this  simple 
assumption,  Hipparchus  sought  to  explain  the  an- 
omaly by  what  has  ever  since  been  known  as  the 
system  of  epicycles.  The  planets  were  assumed  to 
move  in  circular  paths  around  an  immaterial  point, 


50  COPERNICUS. 


which  was  itself  moving  in  a  circle  around  the  earth ; 
just  as  if  the  planets  were  fastened  to  the  rim  of  a 
vast  wheel,  revolving  in  a  plane  passing  through  the 
earth,  while  the  wheel  was  rolling  round  the  crystal 
sphere  which  formed  the  celestial  vault.  Perhaps  the 
wheels  of  the  chariot  of  the  Sun  in  the  Greek  mythol- 
ogy suggested  the  idea ;  and  absurd  as  it  seems  to  us, 
it  was  not  inconsistent  with  the  philosophy  of  motion 
taught  by  Aristotle,  and  universally  held  even  at  the 
time  of  Copernicus.  In  its  more  abstract  f6rm  the 
conception  had  indeed  an  element  of  truth,  and  has 
been  preserved  by  modern  astronomy  in  the  devices 
of  mathematical  analysis  for  computing  a  planet's  ap- 
parent place.  That  such  a  device  would  give  a  gen- 
eral explanation  of  the  stationary  and  retrograde 
phases  in  the  planetary  motions  is  obvious.  But  to 
the  Ptolemaic  school  the  conception  was  of  far  greater 
value  than  this.  By  carefully  collating  and  plotting 
observations,  they  were  enabled  to  determine  the 
periods  of  revolution  both  in  the  epicycle  and  in  the 
cycle,  and  thus  they  calculated  tables  predicting  the 
planets'  positions;  which,  although  vastly  inferior 
both  in  accuracy  and  reach  to  similar  tables  in  our 
nautical  almanacs,  were  wonderful  achievements  for 
the  time,  and  tended  to  give  great  confidence  in  the 
theory  on  which  the  calculations  were  based. 

To  rude  observation  the  motions  of  the  sun  and 
moon  are  far  more  regular  than  those  of  the  planets ; 
and  Hipparchus  was  able  to  explain  the  anomalies, 
so  far  as  they  were  known  to  him,  by  a  theory  of 
eccentrics  which  placed  the  earth,  not  at  the  centre 
of  the  circles  around  which  these  great   luminaries 


COPERNICUS.  5 1 


moved,  but  at  another  point  some  distance  from  the 
centre,  called  the  equant.  As  before,  the  conception 
was  perfectly  definite,  and  received  a  quantitative  ex- 
pression. The  position  of  the  earth  with  regard  to 
the  centre  of  motion  was  determined,  the  points  of 
apogee  and  perigee  in  the  heavens  were  marked  out, 
and  from  these  data  Hipparchus  calculated  tables  of 
the  sun  and  moon.  In  the  time  of  Ptolemy,  when 
the  inequalities  of  the  motions  of  all  the  heavenly 
bodies  were  better  known,  it  became  necessary  to  add 
epicycle  to  eccentric  in  order  to  reconcile  the  obser- 
vations ;  and  the  result  was  a  most  complex  system, 
which  is  graphically  described  by  Milton :  — 

"  .  .  .  how  gird  the  sphere 
With  centric  and  eccentric  scribbled  o'er  — 
Cycle  in  epicycle,  orb  in  orb  !  " 

This  was  the  system  in  which  Copernicus  was  edu- 
cated, and  by  whose  traditions  and  methods  he  must 
have  been  more  or  less  bound.  It  would  be  very 
easy  to  misrepresent  this  system,  and  thus  to  under- 
value the  work  of  Copernicus,  by  showing  how  ab- 
surd and  childish  were  the  theories  he  overthrew. 
In  many  of  the  materialistic  aspects  in  which  it  was 
presented  by  classical  writers,  with  its  mechanism  of 
crystalline  spheres,  it  does  seem  as  if  the  Ptolemaic 
system  must  have  appeared  to  thinking  men  even 
then  incredible  and  monstrous ;  and  one  sympathizes 
with  the  King  of  Castile,  who,  when  the  system  was 
explained  to  him,  is  said  to  have  remarked  that,  "if 
God  had  consulted  him  at  the  Creation,  the  universe 
would  have  been  made  on  a  better  and  simpler  plan." 


52  COPERNICUS. 


But  when  regarded  abstractly,  as  the  resolution  of 
unequal  motions  of  the  heavenly  bodies  into  two  or 
more  equable  circular  motions,  it  was  not  only  a  legi- 
timate scientific  method,  but  is  closely  analogous  to 
the  empirical  methods  followed  at  the  present  day  to 
connect  a  series  of  observations  in  any  department 
of  physical  science  when,  as  is  usually  the  case,  the 
dynamical  causes  are  unknown;  and,  as  before  inti- 
mated, is  essentially  the  same  method  which  is  fol- 
lowed by  the  modern  astronomer  when  he  resolves 
unequal  motions  into  a  series  of  terms  or  expressions 
of  partial  motions  involving  the  trigonometric  values 
of  circular  arcs. 

This  point,  which  has  been  so  well  made  by 
Whewell,  should  be  strongly  emphasized.  The  dy- 
namical law  which  governs  the  motions  of  the  heav- 
enly bodies  was  wholly  unknown  until  discovered  by 
Newton ;  and  as  a  system  of  calculation  the  theory 
of  Hipparchus  was  not  only  good,  but,  as  Whewell 
adds,  "  no  better  has  yet  been  discovered ;  "  and  the 
maze  of  epicycles  is  simply  the  complexity  which 
the  calculations  of  apparent  place  in  astronomy  al- 
ways present.  Moreover  it  appears  very  plainly 
from  the  writings  of  Ptolemy  that  his  school  regarded 
the  whole  machinery  of  epicycles  and  eccentrics  as 
imaginary,  and  used  them  simply  as  devices  for  the 
graphical  representation  of  apparent  motions.  As 
such  they  are  true  expressions,  and  the  best  that 
have  been  yet  devised.  Indeed  more  than  one  half 
of  our  modern  physics  rests  on  no  better  basis  to- 
day. We  have  learned,  however,  to  dissociate  our 
partial  generalizations  from  the  material  symbols  in 


COPERNICUS.  53 


which  they  find  expression,  and  are  content  to  use 
these  aids  as  guides  so  long  as  they  lead  us  aright, 
and  to  wait  until  advancing  knowledge  shall  give  to 
them  a  wider  and  a  fuller  significance.  The  tendency 
among  the  ancients  was  the  very  reverse  of  this.  They 
sought  to  materialize  everything,  as  their  mythology 
so  plainly  shows.  But  at  the  same  time  we  have 
the  best  of  evidence,  as  in  the  works  of  Ptolemy,  that 
their  more  gifted  minds  rose  superior  to  this  spirit, 
and  were  able  to  discern  the  true  ideal  under  the 
conventional  dress  of  the  symbols  they  habitually 
employed ;  and  it  may  be  questioned  whether  the 
"  crystalline  spheres  "  by  which  in  the  imagery  of 
their  poets  the  complex  motions  of  the  heavens  were 
maintained  are  one  whit  more  absurd  than  the  "  lumi- 
niferous  ether,"  without  substance  but  with  indefinite 
elasticity,  with  which  modern  science  has  filled  the 
inter-planetary  spaces. 

If  we  would  appreciate  what  Copernicus  achieved 
we  must  remember  that  he  was  educated  in  the  sys- 
tem whose  striking  features  we  have  been  attempting 
to  sketch,  —  a  system  which  had  all  the  authority  of 
tradition,  all  the  charm  of  antiquity,  all  the  attrac- 
tions of  learning,  and  beneath  its  conventional  sym- 
bols all  the  sanctions  of  sound  philosophy  and  all  the 
spirit  of  true  science. 

We  are  familiar  with  the  outlines  of  the  Coper- 
nican  system,  and  I  trust  are  now  prepared  to  see 
clearly  just  what  this  great  master  contributed  to  the 
world's  real  knowledge,  just  how  far  his  keen  intellec- 
tual vision  was  able  to  penetrate  the  darkness  of  the 
then  unknown.     It  can  be  stated  in  a  few  words ;  for 


54  COFERNICUS. 


the  offering  which  any  man,  however  great,  can  bring 
to  the  altar  of  truth,  though  relatively  it  may  be 
large,  is  always  absolutely  very  small. 

Amidst  the  complexities  of  the  apparent,  Coperni- 
cus discovered  the  simplicity  of  the  real.  He  saw 
law  under  inequalities,  regularity  under  variation, 
order  under  confusion ;  and  having  gained  a  glimpse 
of  the  true  structure  of  the  solar  system,  he  showed, 
by  a  careful  comparison  of  the  theory  with  observa- 
tions, that  the  facts  of  nature  harmonized  with  this 
conception.  The  large  knowledge,  the  grand  con- 
ception, the  scrupulous  confirmation,  —  these  were 
the  essential  and  inseparable  stages  of  this  grand  dis- 
covery. 

Popular  writers  on  astronomy  often  lay  great  stress 
on  the  statement  that  a  heliocentric  hypothesis  was 
a  favorite  tenet  among  the  disciples  of  Pythagoras, 
and  therefore  not  original  with  Copernicus.  But  if 
they  cite  this  well-known  fact  in  disparagement  of 
the  work  of  the  great  father  of  modern  astronomy, 
they  must  wholly  misconceive  the  character  of  a 
scientific  induction.  Those  speculative  philosophers 
of  antiquity  did  not  place  the  sun  in  the  centre  of 
the  solar  system  on  any  basis  of  facts,  but  merely  as 
an  idle  fancy  by  which  they  sought  to  pay  honor  to 
the  sun-god.  How  utterly  different  with  the  system 
of  Copernicus  !  This  was  not  only  an  inference  from 
the  largest  knowledge  of  facts  which  the  best  scholar 
of  his  age  could  gain,  but  was  also  an  inference  veri- 
fied by  observation,  and  by  the  most  exact  meas- 
urements which  could  then  be  made.  Unverified 
hypotheses  are  accounted  of  no  value  in  exact  science, 


COPERNICUS.  55 


and  in  the  opinion  of  competent  judges  no  such  an- 
ticipations in  the  least  detract  from  the  merit  of  a 
real  discovery. 

It  is  not  the  least  among  the  noble  qualities  of  this 
hero  of  science  that  throughout  all  his  work  he  dis- 
played such  deep  humility  of  spirit  and  such  profound 
reverence  for  truth.  His  system  must  have  been 
matured  soon  after  he  settled  at  Frauenburg,  if  not 
before.  It  was  a  vision  of  his  youth  over  which  he 
thought  and  worked  for  forty  years  before  he  told  it 
to  the  world.  He  did  not  hasten  like  a  young  knight 
to  slay  the  dragon  which  had  guarded  so  long  the 
opening  of  the  pathway  to  the  great  treasure.  He 
did  not  at  once  enter  the  lists  against  the  defenders 
of  old  dogmas,  because  they  were  antiquated  and 
seemed  to  him  erroneous.  Truth  was  sacred ;  but 
so  was  just  authority,  so  was  noble  learning,  so  were 
old  institutions.  And  truth  could  wait;  and  truth  did 
wait,  fresh  and  unimpaired,  long,  long  years.  In  those 
lonely  lodgings  at  Allenstein  amidst  the  humblest 
pastoral  and  charitable  duties,  he  questioned  night 
after  night  that  vision  of  his  youth,  multiplying  ob- 
servations and  repeating  calculations,  until  the  truth 
grew  upon  him  with  such  conviction  that  he  could 
no  longer  be  silent;  and  then  he  declared  it,  in  spite 
of  interest,  in  spite  of  opposition,  in  spite  of  contumely, 
in  spite  of  persecution. 

In  the  long  record  of  illustrious  men  who  have 
devoted  their  lives  to  the  advancement  of  knowledge 
for  truth's  sake  alone,  I  know  of  no  incident  more 
impressive,  more  truly  sublime,  than  that  which  is 
narrated  of  the  death  of  Copernicus.  The  forty 
5 


56  COPERNICUS. 


years  of  patient  labor  in  confirmation  of  the  early- 
vision  had  passed.  The  book  had  been  written,  and 
under  great  opposition  had  been  printed  at  Nurem- 
berg. The  last  revisions  had  been  made ;  but  the 
author,  worn  out  at  seventy  years  with  labor  and 
anxiety,  lay  dying  without  any  token  of  the  travail 
of  his  soul.  Indeed  reports  have  come  that  bigotry 
has  succeeded  in  stopping  the  publication  for  which 
his  life  has  been  spent,  and  all  hope  has  fled,  — when 
at  the  last  moment  a  special  messenger  arrives,  and 
places  in  the  hands  of  Copernicus  the  long  expected 
volume  fresh  from  the  press.  The  dying  man  is  just 
able  to  return  a  sign  of  recognition,  and  whisper  the 
final  prayer,  "  Nunc  dimittis  servum  tuum,  Dom- 
INE ! " 

Were  study  always  conducted  in  the  spirit  in  which 
that  book  was  written,  the  harmony  of  all  real  knowl- 
edge would  become  clearly  manifest.  In  the  dedi- 
cation of  the  work  "  De  Revolutionibus  Orbium 
COELESTIUM "  to  Pope  Paulus  III.,  Copernicus  ex- 
pressly states  that  he  has  kept  his  book  by  him 
for  four  times  the  nine  years  recommended  by  Hor- 
ace ;  and  remarks  that  "  the  study  of  a  philosopher 
is  to  seek  out  truth  in  all  things  so  far  as  is  permitted 
by  God  to  human  reason." 

The  Copernican  system  was  not  at  once  generally 
accepted.  Long  cherished  doctrines  with  their  pre- 
scriptive rights  are  not  so  readily  set  aside ;  nor  is 
it  well  that  they  should  be.  But  the  system  did  very 
soon  receive  from  astronomers  that  form  of  recog- 
nition which  would  most  have  pleased  its  author. 
In  155 1  Rcinhold  published  tables,  or"  ephemerides," 


COPERNICUS.  57 


as  they  are  usually  called,  based  on  the  principles  of 
Copernicus,  whose  verified  predictions  tended  greatly 
to  strengthen  his  theory ;  and  the  demonstration  was 
complete  when  in  1610  Galileo's  new  telescope  re- 
vealed to  sight,  in  the  system  of  Jupiter's  satellites,  a 
model  on  a  small  scale  of  the  solar  system  according 
to  the  views  of  Copernicus,  and  not  long  after  showed 
that  Venus  had  phases  like  the  moon,  thus  making 
visibly  manifest  the  planet's  relation  to  the  sun ;  so 
that  in  less  than  a  century  after  the  death  of  its  au- 
thor, in  spite  of  prejudice  and  in  spite  of  theological 
rancor,  the  heliocentric  theory  was  almost  everywhere 
received  by  learned  men  as  an  established  doctrine 
of  astronomical  science.  It  is  a  striking  illustration, 
however,  of  the  conservatism  of  philosophical  thought 
that  Lord  Bacon,  who  lived  until  1628,  long  after  the 
decisive  discoveries  of  Galileo,  never  gave  his  assent 
to  the  Copernican  doctrine,  and  even  Descartes,  who 
lived  until  1650,  gave  to  it  at  most  only  an  implied 
recognition,  rejecting  the  form  while  he  adopted  the 
substance. 

We  can  readily  account  for  the  position  of  Des- 
cartes, who  had  a  theory  of  his  own  which  seemed 
to  him  to  include  all  that  Copernicus  had  discovered ; 
but  we  cannot  but  be  surprised  that  Bacon  was  so 
blind.  It  is  one  thing,  however,  to  think  and  write 
learnedly  about  induction,  and  another  thing  to  make 
discoveries.  Bacon  was  a  metaphysician,  not  a  phys- 
icist, much  less  an  astronomer.  He  had  not  the 
familiarity  with  nature  by  which  alone  an  insight  into 
her  methods  and  processes  can  be  gained.  He  could 
not  therefore  comprehend  the  vision  of  Copernicus, 


58  COPERNICUS. 


and  it  seemed  to  him  a  dream.  To  his  introspective 
mind  the  order  and  finish  of  the  Ptolemaic  system 
had  a  great  charm ;  and  he  was  bound  hand  and  foot 
by  traditions  while  protesting  against  them.  Should 
we  have  been  wiser?  And  may  not  his  experience 
lead  us  not  only  to  honor  more  highly  the  great  man 
whose  character  I  have  sought  to  portray,  but  also 
to  appreciate  more  fully,  and  value  more  highly,  that 
wonderful  power  by  which  he  accomplished  such 
great  results? 


TYCHO   BRAHE.  pq 


LECTURE    III. 

THE    INDUCTION    OF   NEWTON. 

DURING  the  fifty  years  that  followed  the  death 
of  Copernicus,  preparations  were  being  made 
for  another  great  advance  in  the  theory  of  astron- 
omy. These  preparations  consisted  chiefly  in  the 
extension  of  observations,  the  calculation  of  tables, 
the  improvement  of  methods, —  all  resulting  in  the 
collection  of  fuller  and  more  accurate  data  in  regard 
to  the  motions  of  the  heavenly  bodies.  A  very  skil- 
ful observer  appeared,  the  accuracy  of  whose  meas- 
urements exceeded  anything  that  had  yet  been 
obtained.  Copernicus  had  declared  to  a  pupil,  who 
was  disturbed  about  single  minutes,  that  "  if  he  could 
be  sure  to  ten  minutes  of  space,  he  should  be  as 
much  delighted  as  Pythagoras  was  when  he  dis- 
covered the  property  of  the  right-angled  triangle ;  " 
but  it  was  claimed  for  Tycho  Brahe  that  an  error  of 
eight  minutes  in  his  observations  was  impossible. 

In  the  last  year  of  his  life  at  Prague  Tycho  re- 
ceived into  his  observatory,  as  an  assistant,  a  young 
man  named  Johann  Kepler,  who  with  these  eight 
minutes,  to  use  his  own  boastful  words,  was  able  to 
reconstruct  the  whole  of  astronomy.  There  could  not 
be  a  greater  contrast  than  that  between  Copernicus 


60  KEPLER. 

and  Kepler,  —  the  one,  the  ideal  philosopher;  the 
other,  a  veritable  astronomical  Don  Quixote,  turn- 
ing what  he  must  have  known  to  have  been  a  dishon- 
est  penny  by  astrology  in  his  youth,  and  in  his  mature 
manhood  discussing  like  a  Lothario  the  qualifications 
of  eleven  different  damsels  to  become  his  second 
wife.  There  never  was  a  wilder  imagination  than 
that  of  Kepler,  and  he  gave  it  full  rein.  The  wisest 
of  men  have  doubtless  at  times  idle  fancies ;  but  then 
they  have  the  wisdom  to  keep  their  folly  to  them- 
selves, or  at  least  to  their  homes.  Kepler,  on  the 
other  hand,  seems  to  have  had  no  sense  of  decorum. 
He  not  only  entertains  and  cherishes  the  most  ab- 
surd speculations,  but  he  publishes  them  all  to  the 
world ;  so  that  his  voluminous  works  are  a  most 
singular  medley  of  sound  thoughts  and  unmitigated 
nonsense.  But  beneath  all  this  there  is  the  true  sci- 
entific spirit.  He  submits  his  ridiculous  conceptions 
to  the  test  of  experience,  and  rejects  them  at  once 
if  they  do  not  stand  the  trial.  He  displays  without 
reserve  all  the  inner  processes  of  his  thoughts,  ex- 
aggerating his  follies,  and  parading  his  conceits  like  an 
actor;  and  this  makes  his  works  a  curious  study  of 
the  inductive  method  of  reasoning;  for  among  all 
these  wild  guesses  he  discovered  three  great  truths, 
which  have  ever  since  been  known  as  Kepler's  Laws, 
and  which  will  render  his  name  honored  so  long  as 
astronomy  is  studied. 

Copernicus  had  divined  the  great  central  feature 
of  the  solar  system,  but  he  was  trammelled  to  the 
last  by  the  Aristotelian  dogmas  in  regard  to  the  na- 
ture of  motion,  and    assumed   throughout   that  the 


KEPLER.  6l 

heavenly  bodies  must  maintain  an  equable  circular 
motion  in  their  orbits ;  and  in  order  to  explain  the 
obvious  anomalies  which  remained,  even  on  his  helio- 
centric theory,  he  was  obliged  to  retain  the  system 
of  eccentrics  and  epicycles  of  the  Ptolemaic  school, 
although  very  greatly  reduced  in  proportions.  This 
was  a  manifest  blemish  on  the  Copernican  system ; 
but  these  devices  were  evidently  regarded  by  Coper- 
nicus as  temporary  modes  of  representing  the  irreg- 
ularities, for  the  purposes  of  computation.  And  it 
must  be  remembered  that  in  physical  science  appar- 
ent irregularities  are  inseparable  from  observation 
and  experiment ;  and  that  the  most  conspicuous  feat- 
ure of  modern  astronomy  is  the  discussion  of  just 
such  seeming  discrepancies,  only  of  course  of  a  much 
lower  order  of  magnitude.  In  reducing  the  magni- 
tude of  the  anomalies  Copernicus  recognized  that 
he  was  approaching  a  true  theory ;  and  in  the  study 
of  nature  this  is  all  any  man  is  permitted  to  do.  The 
inmost  shrine  cannot  be  entered ;  and  Copernicus 
did  not  feel  the  necessity  of  reconciling  his  empirical 
methods  with  modern  dynamics. 

Kepler  had  no  better  knowledge  than  Copernicus  of 
the  laws  of  motion,— although  he  was  a  younger  man 
by  seven  years  than  Galileo,  and  the  experiments 
of  the  Pisan  professor  on  falling  bodies,  and  his  sar- 
castic attacks  on  the  notions  of  the  Aristotelians,  had 
been  published  long  before  the  famous  laws  of  plan- 
etary motion  were  discovered.  Kepler  not  only  held 
to  the  dynamical  conceptions  of  Aristotle,  but  put 
them  into  the  most  grotesque  guise,  likening  the 
planets  to  huge  animals  rushing  through  the  skies. 


62  KEPLER. 

He  was  not,  however,  hampered  by  deference  to  dog- 
mas of  any  kind.  He  had  no  more  respect  for  a 
circle  than  for  any  other  curve  ;  and  since  an  oval, 
like  a  circle,  returns  upon  itself,  and  would  thus  obvi- 
ously satisfy  one  fundamental  condition  of  a  planet's 
orbit,  he  inquired,  with  the  aid  of  careful  plottings 
and  computations,  how  far  observations  of  positions 
in  the  case  of  the  planet  Mars  could  be  satisfied  on 
the  assumption  of  an  oval  orbit. 

In  the  first  place  he  found  that  by  considering  the 
plane  of  the  planet's  orbit  with  reference  to  the  sun 
alone,  a  position  could  be  given  to  this  plane  from 
which  the  planet  had  none  of  the  librations  which 
both  Ptolemy  and  Copernicus  had  attributed  to  it. 
Copernicus,  influenced  evidently  by  his  Ptolemaic 
education,  had  assumed  that  the  orbits  of  the  planets 
must  have  some  connection  with  the  plane  in  which 
the  earth  moved  ;  and  this  simple  step  of  Kepler's 
at  once  freed  the  heliocentric  theory  from  the  ma- 
chinery of  epicycles  with  which  Copernicus  had  left 
it  encumbered. 

But  the  eccentrics  remained,  for  they  were  facts 
of  nature ;  and  it  was  then  apparent  that  the  planet 
did  not  have  an  equable  motion  in  its  orbit,  as  had 
been  until  then  assumed ;  so  that  with  the  epicycles 
the  old  dogma  of  equable  circular  motions  was  ban- 
ished forever  from  astronomy.  Thus  freed  from  a 
blinding  prejudice,  Kepler  was  soon  able  to  take  a 
great  step  forward.  In  studying  the  conditions  which 
on  the  new  theory  regulated  the  changing  velocity 
of  the  planet's  motion  in  different  parts  of  its  orbit, 
he  discovered  what  has  since  been  known  as  Kepler's 


KEPLER'S   LAWS.  63 


"  Second  Law,"  that  the  areas  described,  or  swept, 
by  the  line  drawn  from  the  planet  to  the  sun  are 
always  equal  in  equal  times,  or  are  proportional 
to  the  durations  of  the  motion.  The  "First  Law," 
that  the  orbits  of  the  planets  are  true  ellipses, 
of  small  eccentricity,  with  the  sun  at  one  of  the  foci, 
was  not  reached  until  some  time  after  the  "  Second 
Law,"  and  the  step  between  the  two  was  a  very  long 
one  for  Kepler.  He  tried  all  sorts  of  hypotheses 
of  circular  and  oval  orbits  before  he  hit  on  what 
would  seem  to  us  the  most  obvious  conception  of 
all ;  and  the  detailed  history  of  his  struggles  with 
this  problem  occupies  thirty-nine  chapters  of  his 
work  "  De  Stella  Martis.  "  The  "  Third  Law,"  that 
the  squares  of  the  periodic  times  of  the  planets  are 
proportional  to  the  cubes  of  the  solar  distances, 
had  in  Kepler's  mind  no  logical  connection  with  the 
first  two,  but  was  the  one  valuable  result  of  the  ex- 
travagant and  often  preposterous  speculations  which 
he  narrates  at  great  length  in  his  book  on  "  The 
Harmonies  of  the  Universe." 

There  is  a  great  deal  in  Kepler's  character  which 
might  naturally  impair  that  respect  for  the  scientific 
investigator  which  the  graces  of  Copernicus  have 
done  so  much  to  establish.  It  seems  inscrutable  that 
such  a  "  krank,"  as  Kepler  appears  in  a  large  part  of 
what  he  wrote,  should  have  accomplished  such  great 
results;  and  it  would  be  natural  to  judge  the  work 
by  the  man.  But  this  was  not  the  first  case  in  which 
"  God  hath  chosen  the  foolish  things  of  the  world  to 
confound  the  wise;  "  and  it  is  possible  that  just  such 
a  man  was  required  to  break  up  the  superstitions 


64  KEPLER'S   CHARACTER. 

which  the  dogmas  of  Aristotle  had  become.  And 
however  weak  in  some  of  the  relations  of  life,  Kepler 
united  all  the  conditions  of  successful  induction.  He 
had  a  very  large  knowledge  of  astronomical  facts,  and 
was  familiar  with  all  their  limitations.  He  had  an 
exuberant  imagination,  and  great  fertility  of  invention. 
He  was  loyal  to  nature,  and  never  harbored  his  errors 
when  once  refuted.  As  Whewell  very  justly  says, 
"Kepler  certainly  was  remarkable  for  the  labor  which 
he  gave  to  such  self-refutations,  and  for  the  candor 
and  copiousness  with  which  he  narrated  them;  his 
works  are  in  this  way  extremely  curious  and  amus- 
ing, and  are  a  very  instructive  exhibition  of  the 
mental  process  of  discovery." 

To  illustrate  the  characteristic  features  of  the  in- 
ductive method  here  referred  to  is  the  chief  object  of 
these  lectures ;  and  I  trust  that  the  story  of  Kepler 
has  made  prominent  three  essential  conditions  of 
success :  first,  a  large  knowledge  of  facts,  based  on 
an  intimate  acquaintance  with  the  phenomena  of  na- 
ture; secondly,  a  fertile  imagination,  ready  to  sug- 
gest the  possible  relations  of  these  facts ;  thirdly,  a 
conscientious  scientific  spirit,  which  submits  every 
hypothesis  to  the  test  of  observation  or  experiment. 

The  laws  of  Kepler  were  purely  formal ;  that  is, 
they  were  expressions  of  facts  or  relations  for  which 
no  explanation  was  given,  or  could  be  given  at  that 
time.  It  was  a  fact  that  the  planets  moved  in  ellip- 
tical orbits  ;  it  was  a  fact  that  the  radius  vector  swept 
over  equal  areas  in  equal  times ;  it  was  a  fact  that  the 
squares  of  the  periodic  times  were  proportional  to 
the  cubes  of  the  sun's  mean  distance;  and  the  cir- 


FORMAL  AND  DYNAMICAL  LAWS.       6$ 

cumstance  that  these  facts  were  learned  by  inference, 
and  not  by  direct  observation,  does  not  alter  their  re- 
lation to  the  scheme  of  knowledge.  They  are  in  no 
respect  efficient  causes.  They  are  simply  facts  and 
nothing  more,  and  to  Kepler  they  were  wholly  dis- 
connected facts ;  and  this  distinction  between  a  for- 
mal or  phenomenal  law,  which  merely  expresses  a 
general  fact  of  nature,  and  a  dynamical  law,  which 
gives  the  mode  of  action  of  an  efficient  cause,  corres- 
ponds to  a  most  important  step  in  the  progress  of 
science.  We  can  distinguish  three  stages  in  this  pro- 
gress :  first,  the  phenomenal  stage,  in  which  only 
isolated  facts  are  observed  and  recorded ;  secondly, 
the  formal  stage,  in  which  facts  of  general  relation- 
ship are  discovered ;  thirdly,  the  dynamical  stage,  in 
which  the  relations  are  traced  to  some  efficient  cause. 
Astronomy  was  raised  to  its  second  stage  by  Hippar- 
chus,  to  its  third  stage  by  Newton.  Until  the  end 
of  the  seventeenth  century  it  was  still  in  the  formal 
stage,  and  the  discoveries  of  Kepler  did  not  alter  its 
position,  although  they  prepared  the  way  for  the 
great  advance  which  was  soon  to  follow.  According 
to  Kepler's  loftiest  conceptions  the  planets  moved  in 
the  manner  which  he  had  discovered  simply  because 
it  was  their  nature  so  to  move.  But  a  far  more  gifted 
seer  was  soon  to  come,  who  should  show  that  the  laws 
of  Kepler  were  the  necessary  and  very  partial  re- 
sults of  the  action  of  a  force  which  controlled  the 
universe. 

If  after  his  work  was  done  Kepler  had  been  told 
that  in  less  than  a  century  the  laws  he  had  discovered 
would  be  shown  to  be  merely  phases  of  the  action  of 


66  KEPLER'S   IDEA   OF   FORCE. 

universal  gravitation,  there  can  be  little  doubt  that  he 
would  have  regarded  the  prophecy  as  grandiloquent 
nonsense.  Kepler  associated  no  clear  conception 
with  the  word  "  force,"  and  did  not  recognize  a  force 
of  gravitation.  By  Kepler,  and  by  all  scholars  before 
him,  as  well  as  by  many  after  him,  the  word  "  force  " 
was  used  to  denote  any  manifestation  of  energy,  which 
might  vary  widely  not  only  in  its  nature  but  also  in 
its  mode  of  action.  There  were  forces  innumerable, 
each  with  its  own  special  virtue  and  mode  of  action. 
It  was  obvious  then  as  now  that  muscular  force  would 
produce  motion,  and  that  a  moving  body  would  exert 
force  ;  but  there  were  no  clear  conceptions  of  the  re- 
lation of  motion  to  force.  A  stone  fell  to  the  ground, 
not  because  it  was  pulled  by  a  force  which  we  now 
call  gravity,  but  because  it  was  the  tendency  of  heavy 
bodies  to  move  downward,  through  a  virtue  residing 
in  the  body  itself,  not  in  the  earth.  It  must  have  been 
known  to  Kepler  that  while  he  was  at  work  on  the 
theory  of  Mars  an  Italian  named  Galileo,  with  whom 
subsequently  he  maintained  a  friendly  correspond- 
ence, had  been  making  some  curious  experiments  on 
swinging  pendulums  and  falling  bodies,  which  were 
subversive  of  all  the  old  mechanical  notions ;  but  he 
did  not  dream  that  they  had  any  bearing  on  his 
studies.  Yet  Galileo  was  doing  for  mechanics  almost 
precisely  what  Kepler  was  doing  for  astronomy,  and 
the  labors  of  both  men  were  the  necessary  prelude  to 
the  induction  of  Newton.  In  order  that  we  may  the 
better  understand  the  bearing  of  this  new  and  con- 
verging line  of  investigation  it  may  be  well  for  me  to 
review  very  briefly  the  fundamental  conceptions  of 


FORCE   AND   MOTION.  67 


the  modern  theory  as  to  the  relations  of  motion  and 
force. 

We  know  nothing  more  about  the  origin  of  force 
than  our  fathers,  but  we  have  a  very  clear  idea  about 
the  uniformity  of  its  manifestation.  Force,  however 
produced,  always  manifests  itself  either  as  a  pull  or  a 
push,  and  no  matter  what  may  be  the  circumstances, 
this  pull  or  push  varies  only  in  strength.  The  force 
may  be  produced  by  muscular  action ;  it  may  be  due 
to  electrical  excitation ;  it  may  be  an  effect  of  mag- 
netism;  it  may  be  caused  by  heat;  it  may  be  grav- 
ity ;  but  in  all  these  cases  the  ultimate  effect  is  a  pull 
or  a  push.  We  do  not,  of  course,  by  this  analysis, 
remove  in  the  least  degree  the  mystery  which  still 
surrounds  the  origin  of  force;  we  know  nothing 
more  about  the  nature  of  gravity  than  we  knew  be- 
fore :  but  we  do  know  that  gravity  acts  as  a  pull  of 
definite  strength ;  and  we  have  made  a  great  advance 
towards  clear  thinking  when  we  have  been  able  to 
banish  from  our  minds  all  the  indefinite  and  mys- 
terious accessories  with  which  the  term  has  been  as- 
sociated, and  whenever  the  word  "  force"  is  used,  to 
think  only  of  a  pull  or  a  push  between  two  definite 
bodies.  So  also  with  motion.  It  would  be  easy  to 
bewilder  the  imagination  by  attempting  to  combine 
the  various  motions  of  which  every  object  on  the  sur- 
face of  the  earth  must  simultaneously  partake;  or 
confuse  the  mind  by  discussing  whether  independent 
motion  in  space  is  oonceivable.  But  in  physics  we 
deal  only  with  relative  motions.  We  do  not  recog- 
nize absolute  rest  or  motion.  An  object  is  at  rest  or 
in  motion  solely  with  reference  to  some  other  object. 


68  FORCE   AND    MOTION. 


A  body,  therefore,  may  be  at  the  same  time  at  rest 
in  relation  to  one  object  and  in  motion  in  regard  to 
another.  If  two  bodies  are  moving  with  relation  to 
each  other  it  is  wholly  arbitrary  which  is  regarded  as 
at  rest  and  which  in  motion.  It  is  not  necessary  to 
dwell  on  illustrations  of  these  points,  which  the  mov- 
ing trains  on  our  railroads  so  frequently  bring  to 
mind.  Rest  and  motion  in  mechanics  are,  therefore, 
simply  relative  states,  and  should  only  be  considered 
from  this  point  of  view.  Never  think  of  motion  as 
an  attribute  of  a  body,  but  only  as  change  of  place 
with  reference  to  some  other  body.  If  the  old  Greeks 
could  have  realized  this  simple  conception  the  prog- 
ress of  astronomy  would  have  been  hastened  by  at 
least  a  thousand  years. 

It  will  now  be  seen  to  be  an  obvious  phase  of  the 
fundamental  conception,  that  the  same  body  may  par- 
take of  several  motions  at  once,  and  that  each  of  these 
motions  will  be  entirely  independent  of  the  others, 
and  uninfluenced  by  them ;  so  that  the  resulting  path 
and  final  goal  will  be  simply  the  combined  effect  of 
all.  This  conclusion,  if  not  at  once  obvious,  will  ap- 
pear if  it  is  remembered  that  according  to  the  fun- 
damental conception  of  motion,  a  body  assumed  to 
be  at  rest  in  relation  to  several  other  bodies  assumed 
to  be  in  motion  is  in  the  same  condition  towards 
each  one  as  if  these  assumed  states  were  reversed ; 
and  hence,  that  its  relations  to  the  several  bodies 
must  be  as  independent  in  one  state  as  in  the  other. 
Thus  arise  all  the  familiar  principles  of  the  composition 
and  resolution  of  motions,  which,  however  complex  in 
some  of  their  applications,  are  very  simple  in  theory. 


DIRECTION.  69 


As  with  motion,  so  also  in  regard  to  direction,  we 
have  only  relative  knowledge.  It  is  useless  to  inquire 
whether  we  could  form  any  idea  of  direction  indepen- 
dently of  the  objects  around  us ;  and  it  was  merely 
their  limited  acquaintance  with  the  dimensions  of  the 
universe  which  led  the  Greeks  to  speculate  about 
absolute  directions.  Upward  and  downward  have 
reference  solely  to  the  earth ;  and  directions  can  be 
known  only  in  relation  to  the  positions  or  features  of 
material  bodies.  Practically,  we  refer  both  direction 
and  motion  to  the  earth,  with  its  fixed  axis  and  con- 
stant time  of  rotation,  and  with  well  marked  features 
on  its  surface ;  and  we  come  to  associate  our  ideas  of 
motion  and  direction  solely  with  this  standard.  But 
we  should  bear  in  mind  that  this  standard,  though 
natural,  is  arbitrary,  —  that  other  standards  might  be 
used,  and  are  used  in  astronomy.  When  in  analytical 
geometry  or  crystallography  we  refer  directions  and 
positions  to  a  set  of  arbitrary  lines  called  axes,  we 
merely  do  for  our  problems  what  nature  has  done 
for  our  every-day  life,  by  placing  us  on  a  globe  with 
definite  outlines  which  set  bounds  to  our  habitation, 
and  fixed  limits  on  which  our  thoughts  may  rest. 
To  the  young  student  of  mathematics  all  this  sys- 
tem of  co-ordinates,  with  the  arbitrary  transforma- 
tions, seems  very  artificial ;  but  they  are  essential 
conditions  of  clear  thought ;  and  it  was  the  want  of 
the  very  conception  which  they  embody  which  made 
the  method  of  Euclid  so  limited  in  its  applications. 

Few  works  that  have  come  down  to  us  so  strik- 
ingly illustrate  the  fertility,  acuteness,  and  versatility 
of  the  Greek  mind  as  the  "  Geometry  of  Euclid  ;  "  and 


70      DEFECT  OF  THE  GREEK  GEOMETRY. 

it  remains  to  our  time  one  of  the  chief  tools  in  educa- 
tion. As  a  training  in  intellectual  gymnastics  it  is  an 
admirable  study,  but  as  a  means  of  investigating  na- 
ture it  is  practically  useless ;  and  the  defect  of  the 
Greek  geometry,  like  the  defect  of  the  Greek  me- 
chanics, arose  from  seeking  the  fundamental  con- 
ceptions, not  in  the  observation  of  nature,  but  in  the 
accidents  of  thought,  —  although,  from  the  nature  of 
the  subject,  the  first  defect  was,  of  the  two,  far  the 
less  serious  in  its  consequences.  This  defect  appears 
conspicuously  in  Euclid's  treatment  of  the  straight 
line,  which  is  defined  as  the  shortest  distance  be- 
tween two  points ;  leaving  out  of  account  the  funda- 
mental characteristic,  that  of  definite  direction.  The 
Greeks  were,  with  reason,  very  proud  of  their  ge- 
ometry; but  the  science  could  not  measure  the  earth, 
as  its  name  denotes,  much  less  the  heavens,  until  it 
was  re-established  by  Descartes  on  the  basis  of  accu- 
rate conceptions  of  direction.  Even  at  the  present 
day,  since  most  of  us  have  derived  our  knowledge 
of  geometry  either  directly  or  indirectly  from  Euclid, 
it  is  not  unimportant  to  insist  that  direction,  like  mo- 
tion, is  a  fundamental  condition  or  state,  inseparable 
from  material  existence,  whose  relations  we  must  ac- 
cept as  facts  of  observation,  and  not  merely  as  modes 
of  consciousness. 

With  the  fundamental  conceptions  clearly  estab- 
lished, see  how  very  simple  all  the  relations  of  force 
to  motion  at  once  become;  and  how  intelligible,  in 
the  light  of  our  familiar  experience.  If  a  body  is  at 
rest  with  reference  to  another  it  can  be  set  in  motion 
only  by  the  application  of  force,  —  that  is,  by  what 


LAWS   OF   FALLING  BODIES.  J I 

is  the  equivalent  of  a  pull  or  a  push  between  the  two ; 
if  it  is  in  motion  it  can  only  be  brought  to  rest  in  the 
same  way ;  and  to  start  a  body  when  at  rest,  or  to 
stop  it  when  moving,  are,  mechanically,  equivalent 
operations. 

When  a  constant  force  acts  on  a  body  in  the  direc- 
tion of  its  motion,  the  velocity  of  the  motion  must  be 
constantly  accelerated,  because  the  effect  of  the  pull 
at  any  instant  must  be  added  to  the  previous  condi- 
tion. Remembering  that  the  pull  or  push  at  each 
instant  simply  adds  its  effect  to  the  previous  state, 
it  will  be  seen  that  the  laws  of  accelerated  or  re- 
tarded motions  —  including  the  laws  of  falling  bodies 
—  follow  at  once  from  the  fundamental  principles ; 
and  that  acceleration  or  retardation  are  indications  of 
the  action  of  some  force;  and  that  the  amount  of 
acceleration  or  retardation  is  the  measure  of  that 
force.  If  a  body  is  acted  on  by  two  or  more  forces 
at  once,  each  produces  its  effect  independently  of  the 
others,  and  the  final  result  is  found  by  simply  com- 
bining the  several  effects. 

Evidently,  very  complex  problems  may  arise  under 
the  conditions  last  named.  One  of  the  simplest  is 
when  a  bomb-shell  is  thrown  from  a  mortar.  The 
exploding  gunpowder  gives  to  the  ball  a  tremendous 
push  in  a  given  direction,  and  were  it  not  for  the 
pull  of  the  earth  and  the  resistance  of  the  air,  —  which 
last  we  here  leave  out  of  the  account,  —  the  ball,  with 
reference  to  the  gun,  would  move  on  forever  and 
with  a  uniform  velocity;  but  the  moment  it  starts 
from  the  gun  it  begins  to  fall  to  the  earth,  and  falls 
the  same  number  of  feet  in  a  given  time  that  a  stone, 
-  6 


72        PROBLEM  OF  CENTRAL  FORCES. 

or  any  other  object,  would  fall  if  dropped  from  an 
elevation.  The  actual  path  is  a  combination  of  the 
two  motions,  and  would  be  a  parabola  were  it  not 
for  the  resistance  just  referred  to.  Another  and  some- 
what similar  problem  assumes  great  importance  from 
its  astronomical  relations.  A  body  is  moving  with 
reference  to  another,  and  much  more  massive,  object, 
which  for  distinction  we  will  call  the  central  body,  — 
not  directly  to  or  from  it,  but  on  a  line  which  leaves 
the  central  body  on  one  side  at  a  greater  or  less 
distance.  On  this  moving  mass  the  central  body 
exerts  a  constant  pull.  What  will  be  the  effect? 
This  will  depend  on  the  strength  of  the  pull ;  but, 
in  general,  the  path  assumed  by  the  moving  body 
will  be  that  of  one  of  the  conic  sections,  drawn 
round  the  central  body  as  the  nearer  focus,  and  in  a 
plane  containing  both  this  centre  of  force  and  the 
original  path.  If  the  force  were  comparatively  feeble 
the  body  would  describe  the  arc  of  an  hyperbola, 
and  fly  off  on  a  new  course  in  the  direction  of  the 
asymptote  to  this  curve ;  but  if  the  force  were  be- 
yond certain  limits  the  path  would  be  a  circle  or  an 
ellipse  returning  on  itself;  and  we  should  then  have 
the  counterpart  of  the  motions  of  the  planets. 

In  this  connection  it  is  to  no  immediate  purpose  to 
inquire  what  was  the  cause  of  the  primitive  motion, 
unless  as  a  matter  of  curious  speculation  about  world- 
building;  for  the  motion  was  a  primitive  state,  just  as 
much  as  the  chemical  elements  or  any  other  funda- 
mental conditions.  The  solution  of  the  problem  of 
central  forces,  as  it  has  been  called,  is  independent  of 
such  considerations,  and  is  complete  without  them. 


THE   THREE   LAWS   OF   MOTION.  73 


With  our  present  conceptions  of  force  and  motion  it 
seems  perfectly  simple,  and  as  given  in  our  college 
text-books  it  can  be  followed  by  any  scholar  with  a 
moderate  knowledge  of  mathematics ;  but  only  two 
hundred  years  ago  it  taxed  the  best  minds  of  an  age 
remarkable  for  the  powerful  intellects  it  produced. 

From  the  primary  conceptions  of  direction,  motion, 
and  force,  it  would  be  very  easy  to  develop  all  the 
fundamental  principles  of  mechanics,  —  to  show  that 
when  a  pull  or  a  push  acts  between  two  bodies  both 
must  partake  equally  in  the  effect,  or  in  other  words 
that  action  and  reaction  must  be  equal  and  opposite, 
—  to  make  evident  that  the  mass  of  the  bodies,  as 
measured  by  their  weight,  is  a  most  important  factor 
in  the  result,  and  that  the  velocity  imparted  by  a  force 
of  constant  strength,  other  things  being  equal,  must 
be  proportional  to  the  amount  of  material  on  which 
the  force  acts,  —  to  point  out  the  distinction  between 
tension,  or  pressure,  and  work,  or  between  momen- 
tum and  vis  viva,  a  distinction  which,  although  now 
so  familiar,  was  during  the  eighteenth  century  the 
subject  of  a  long  and  warm  controversy  among  the 
most  eminent  mathematicians  of  Europe.  But  these 
points  have  only  an  indirect  bearing  on  my  present 
argument;  and  I  will  close  this  summary  of  essential 
preliminaries  with  the  statement  of  the  three  laws  of 
motion  as  given  by  Newton  in  his  "  Principia."  First 
Law :  Every  body  continues  in  a  state  of  rest,  or  of 
uniform  motion  in  a  straight  line,  unless  acted  on 
by  some  external  force.  Second  Law:  Change  of 
motion  is  proportional  to  the  force  impressed,  and  is 
in   the   line  in  which   the  force  acts.      Third  Law: 


74  GALILEO. 

To  every  action  there  is  always  opposed  an  equal 
reaction. 

Although  at  the  present  day  the  relations  of  force 
to  motion  might  be  summarized  to  advantage  in  more 
general  terms,  yet  these  formulas  show  a  perfectly 
clear  conception,  on  the  part  of  Newton,  of  the  true 
relations,  and  indicate  a  wonderful  advance  in  clear- 
ness of  thought  on  this  subject  between  the  publica- 
tion of  Kepler's  work  "  De  Stella  Martis  "  in  1608, 
and  that  of  the  "  Principia  "  in  1686.  This  is  not  the 
place  to  follow  in  detail  the  history  of  this  progress ; 
but  we  will  touch  on  one  or  two  points,  of  which  the 
summary  we  have  just  given  will  enable  you  to  see 
the  bearings. 

Galileo  —  who  was  born  in  1564,  and  became  a 
teacher  at  the  University  of  Pisa  in  1589  —  laid  the 
foundations  of  modern  mechanics ;  and  chiefly  by 
the  remarkable  series  of  experiments  which  he  made 
at  Pisa  during  the  three  years  (1589-91).  In  gen- 
eral terms  it  may  be  stated  that  Galileo  discovered, 
and  verified  by  experiment  as  formal  laws,  most  of 
the  fundamental  principles  of  dynamics.  He  taught 
that  all  matter  has  weight,  and  that  gravity  and 
levity  are  only  relative  terms.  He  pointed  out  the 
relations  of  the  centre  of  gravity,  and  insisted 
that  weight  was  a  constant  force,  pulling  all  bodies 
towards  the  centre  of  the  earth.  He  maintained  that 
motion  was  the  result  of  force,  and  clearly  enunciated 
the  laws  of  falling  bodies,  —  illustrating  the  theory 
by  experiments  from  the  "Leaning  Tower  of  Pisa" 
which  have  become  memorable  in  the  history  of  sci- 
ence.    He  clearly  distinguished  between  uniform  and 


GALILEO'S   DISCOVERIES.  75 

accelerated  motion.  He  showed  that  motion  caused 
by  a  single  force  is  always  in  a  straight  line,  — that  is, 
in  a  definite  direction;  but  that  under  the  influence 
of  several  forces  a  body  may  move  in  as  many  direc- 
tions at  once,  simultaneously  and  independently.  He 
established  the  principle  of  the  composition  of  forces, 
and  gave  the  true  theory  of  projectiles.  He  distinctly 
recognized,  at  least  by  implication,  the  principles  of 
action  and  reaction,  and  even  of  virtual  velocities. 
His  works  are  full  of  ingenious  demonstrations  of 
mechanical  theorems,  both  theoretical  and  experi- 
mental ;  and  he  was  versatile  as  an  experimenter 
as  he  was  sound  as  a  reasoner.  But  still,  his  results 
were  for  the  most  part  formal,  and  not  co-ordinated 
under  general  principles.  Unquestionably,  the  prin- 
ciples of  Newton's  three  laws  of  motion  may  be  re- 
garded as  implied  in  the  whole  tenor  of  Galileo's 
experiments  and  computations,  but  they  are  no- 
where definitely  formulated  in  his  writings, —  although 
in  the  review  of  the  principles  of  mechanics  which 
he  published  near  the  close  of  his  life  he  shows  much 
more  distinct  conceptions  of  the  nature  and  relations 
of  force  and  motion  than  he  did  in  his  earlier  work. 
This  book,  entitled  "  Dialoghi  delle  Nuove  Scienze," 
and  printed  by  the  Elzevirs  at  Leyden  in  1638, 
gained  universal  admiration,  and  drew  wide  attention 
to  the  subject.  Like  a  well-known  book,  "  Heat  as 
a  Mode  of  Motion,"  which  has  done  a  similar  work 
in  our  own  day,  this  last  and  best  of  the  publications 
of  the  great  Florentine  familiarized  men's  minds 
with  the  interdependence  of  force  and  motion,  which 
up  to  this  time  had  been  only  a  disputed   doctrine 


j6  GALILEO  A  POPULAR  LECTURER. 

known  to  a  few  scholars.  The  works  of  Galileo  were 
among  the  most  important  means  of  education  for 
the  future  Newton,  and  through  them  this  noble 
father  of  mechanical  science,  as  well  as  great  dis- 
coverer in  astronomy,  was  in  fact  one  of  the  chief 
teachers  of  his  far  greater  successor. 

In  estimating  the  ability  of  Galileo  and  the  merit 
of  his  labors,  we  must  remember  that,  like  Coper- 
nicus, he  had  to  contend  with  the  prejudices  among 
all  scholars  in  favor  of  the  dogmas  of  Aristotle; 
which  at  the  time  were  not  only  a  belief  but  a  reli- 
gion. Still,  we  cannot  but  regret  that  so  much  of  the 
energy  of  this  great  originator  was  wasted  in  fruitless 
disputations  with  the  upholders  of  the  old  doctrines, 
whom  he  followed  with  such  pertinacity  and  bitterness 
that  they  became  his  violent  enemies.  In  this,  how- 
ever, he  was  but  taking  the  course  to  which  his  disposi- 
tions and  abilities  inclined  him  ;  for  Galileo  had  a 
most  remarkable  power  both  as  an  expositor  and  as  a 
writer.  He  was  what  we  should  call  a  most  success- 
ful popular  lecturer  ;  and  when,  driven  by  the  old 
schoolmen  from  Pisa,  he  accepted  a  professorship  at 
Padua,  a  hall  holding  two  thousand  persons  was  pro- 
vided to  receive  the  vast  audiences  which  thronged 
to  his  lectures. 

It  was  his  controversial  spirit,  rendered  especially 
irritating  by  the  great  influence  of  his  powerful  utter- 
ance, which  led  to  the  collision  of  Galileo  with  the 
Papal  authorities.  At  heart  he  was  a  good  Catholic 
and  a  faithful  son  of  the  Church.  He  had  many 
friends  among  the  most  influential  of  the  clergy ; 
and  there  can    be   no    question  that  he  would  have 


GALILEO'S   CONFLICT   WITH   THE   CHURCH.       JJ 

been  left  to  teach  as  he  pleased,  and  even  been 
honored  for  his  innovations,  if  only  he  had  avoided 
theological  issues,  instead  of  rushing  into  them. 
There  was  no  need  of  forcing  that  greatly  irritated 
lion  caged  at  the  Vatican  to  show  its  claws.  Neither 
truth  nor  honor  required  it;  and  though  we  may  not 
think  that  a  scholar  can  honorably  hold  an  equivocal 
position  in  regard  to  facts  of  demonstration,  yet  the  dis- 
tinction between  "  ex  hypothesi "  and  "  ex  animo  "  was 
one  which  Galileo  avowedly  accepted.  And  when  he 
violated  his  pledges,  and  again  revived  the  old  issues, 
we  cannot  wonder  that  his  conduct  provoked  censure  ; 
and  it  may  be  questioned  whether  he  was  treated  any 
more  harshly  than  is  many  a  man  at  the  present  day, 
for  a  much  less  departure  from  prescribed  creeds. 

In  the  next  generation  after  Galileo  the  theory  of 
mechanics  became  much  more  clearly  developed,  and 
chiefly  by  his  pupils  or  by  those  whom  he  directly 
influenced.  Of  this  generation,  although  only  surviv- 
ing Galileo  eight  years,  was  Descartes,  one  of  the  most 
powerful  minds  which  the  world  has  ever  produced. 
Descartes,  however,  was  a  metaphysician  rather  than 
a  physicist ;  a  better  reasoner  than  observer ;  a  better 
mathematician  than  experimentalist.  He  never  fully 
entered  into  the  spirit  of  the  inductive  method,  or 
made  any  far-reaching  induction,  —  although  he  spent 
much  time  in  experimental  work,  especially  in  phys- 
iology, and  made  some  notable  discoveries  in  phys- 
ics, particularly  the  cause  of  the  rainbow.  His  theory 
of  vortices,  received  with  great  applause  at  the  time 
as  a  mode  of  explaining  the  motions  of  the  heavenly 
bodies,  and  in  its  essential  features  revived  of  late  in 


78  THE   INFLUENCE   OF   DESCARTES. 


connection  with  molecular  physics,  plainly  shows  that 
Descartes  had  not  a  clear  appreciation  of  the  funda- 
mental conceptions  of  mechanics.  Nevertheless  his 
enunciation  —  for  little  less  can  it  be  called  —  of  the 
principle  of  the  conservation  of  energy  is  an  anticipa- 
tion of  one  of  the  very  latest  results  of  science,  than 
which  none  more  remarkable  can  be  found  in  the  whole 
history  of  speculative  thought;  and  this  prevision  will 
appear  still  more  wonderful  when  it  is  remembered 
that  it  involved  the  assumption  of  molecular  motion, 
with  the  plain  suggestion  that  heat  may  be  a  mani- 
festation of  the  internal  motions  of  material  bodies. 
Nevertheless,  apart  from  his  metaphysical  writings,  the 
great  contribution  that  Descartes  made  to  the  world's 
progress  was  his  geometry,  to  which  we  have  before 
referred,  and  whose  leading  principle  we  have  pointed 
out.  Descartes  not  only  gave  a  new  life  to  this  oldest 
of  the  sciences,  but  he  endowed  it  with  a  power  of 
interpretation  which  has  done  more  than  all  other 
agencies  combined  to  extend  our  knowledge  of  the 
heavenly  bodies. 

Into  a  world  thus  prepared  for  a  great  revelation  of 
knowledge  was  born,  Christmas  day,  1642,  at  the 
close  of  the  very  year  in  which  Galileo  died,  the  child 
who  was  to  render  illustrious  his  father's  homely 
name  of  ISAAC  NEWTON. 

It  is  always  highly  interesting  to  study  the  career 
of  a  man  who  has  fulfilled  an  important  mission,  —  to 
attempt  to  discover  inherited  tendencies  ;  to  trace  the 
influences  by  which  his  mind  was  moulded  ;  to  notice 
early  indications  of  peculiar  power,  even  if  remark- 
able only  because  they  seem  prophetic ;  to  mark  the 


EARLY   LIFE   OF  NEWTON.  79 

guidings  of  opportunities,  if  not  the  leadings  of  Provi- 
dence ;  to  discriminate  between  native  genius  and  ac- 
quired talent;  to  see  force  of  intellect  and  of  will 
rising  superior  to  circumstances ;  or,  what  is  often 
most  singular,  to  find  in  the  limitations  of  mental  en- 
dowments a  more  potent  influence  than  natural  abili- 
ties in  leading  the  specialist  apart  from  the  beaten 
track;  to  realize  what  were  the  conditions  under 
which  the  great  leader  worked,  and  what  were  the 
materials  at  his  command ;  and  finally,  to  learn  how 
small,  after  all,  were  the  single  steps  by  which  he 
attained  success. 

Unfortunately,  we  have  only  the  most  meagre  out- 
lines of  the  early  life  of  Newton.  He  does  not  seem  to 
have  been  a  precocious  child ;  and  the  tales  of  early 
mechanical  skill  are  only  such  as  are  told  of  many  a 
boy  who  has  become  only  an  ordinary  man.  Even  at 
college  —  to  which  he  appears  to  have  been  sent  on 
an  after-thought,  like  the  weakly  son  of  a  New  Eng- 
land farmer  —  there  is  no  evidence  that  he  gained 
great  distinction;  so  that  when,  in  1667,  at  the  age 
of  twenty-five,  two  years  after  he  received  the  Bach- 
elor's degree,  he  was  appointed  Fellow  of  Trinity 
College,  Cambridge  (his  own  college),  we  are  sur- 
prised to  find  him  in  possession  of  a  power  of 
mathematical  analysis  far  in  advance  of  the  best 
mathematicians  of  his  day.  He  himself  tells  us  that 
while  an  undergraduate  he  studied  the  Geometry  of 
Descartes,  which  he  had  some  difficulty  in  mastering; 
and  already  by  his  method  of  fluxions  he  had  vastly 
extended  the  grasp  of  the  new  Cartesian  instrument 
of  research. 


SO  HIS    SYSTEM   OF   FLUXIONS. 

As  is  well  known,  "  Fluxions  "  was  the  name  given 
by  Newton  to  the  Infinitesimal,  or,  as  it  is  now  more 
frequently  called,  the  Differential  and  Integral  Cal- 
culus ;  and  the  advance  made  by  the  introduction  of 
this  new  method  into  geometry  was  incomparably 
greater  than  any  step  which  had  hitherto  been  taken. 
It  was,  moreover,  peculiarly  an  intellectual  achieve- 
ment; and,  although  some  advance  had  previously 
been  made  in  the  mathematical  treatment  of  the  in- 
finitesimal quantities  of  geometry,  especially  by  Fer- 
mat  and  also  by  Barrow,  Newton's  predecessor  in  the 
Lucasian  chair  of  mathematics  at  Cambridge,  yet  the 
improvement  made  by  Newton  was  very  great.  That 
this  improvement  should  have  been  made  by  an 
undergraduate  was  wonderful ;  and  we  find  it  diffi- 
cult to  explain  why  it  did  not  at  once  win  admira- 
tion, and  was  not  widely  proclaimed  and  highly 
honored,  except  on  the  assumption  that  though 
far  in  advance  of  his  instructors,  Newton's  abilities 
and  attainments  were  limited  to  special  lines,  which 
did  not  at  the  time  find  favor  among  the  university 
authorities. 

The  method  of  fluxions,  although  from  this  early 
period  constantly  used  by  Newton  in  his  own  work, 
and  doubtless  taught  by  him  as  Professor  of  Mathe- 
matics, —  an  office  which  he  filled  at  Cambridge  from 
1669  to  1 701,  — was  not  fully  described  in  print  until 
1691,  and  then  not  by  himself;  although  the  prin- 
ciple of  the  method  was  given  in  a  geometrical  form 
in  the  "  Principia"  four  years  earlier.  It  fTius  came  to 
pass  that  in  publication  Newton  was  anticipated  by 
Leibnitz,  who,  in  the  "  Acta  Eruditorum,"   Leipsic, 


THE   CALCULUS   OF   LEIBNITZ. 


1684,  described  essentially  the  same  method,  though 
under  a  different  name  and  with  a  different  notation. 
In  England  Leibnitz  was  accused  of  borrowing  his 
first  conceptions  from  hints  in  letters  of  Newton,  and 
no  little  bitterness  on  both  sides  was  the  result.  But 
in  the  discussion  which  arose,  while  Newton's  priority 
was  established  beyond  a  question,  the  originality  of 
Leibnitz  was  also  made  equally  clear ;  and  it  is  the 
notation  and  forms  of  Leibnitz,  and  not  those  of 
Newton,  which  have  been  retained  in  science. 

We  do  not  know  how  early  Newton  applied  his 
new  calculus  to  the  solution  of  the  so-called  problem 
of  central  forces.  Since  the  principles  of  the  compo- 
sition of  forces  had  been  established  by  Galileo  it 
had  become  evident  that  the  path  of  a  planet  might 
be,  as  we  have  already  pointed  out,  the  resultant  of 
a  primary  motion  of  translation,  modified  by  some 
power  constantly  pulling  the  body  towards  the  centre 
of  motion ;  and  the  question  was,  what  would  be  the 
form  of  the  orbit  under  such  conditions.  Attention 
had  been  drawn  to  this  problem  in  many  quarters, 
but  the  resources  even  of  the  geometry  of  Descartes 
were  not  adequate  to  a  complete  solution.  One  con- 
clusion, however,  quite  plainly  followed  from  the 
third  law  of  Kepler,  —  although  the  complete  demon- 
stration even  of  this  point  was  first  given  by  Newton, 
—  and  this  conclusion  was  that  if  such  a  central  force 
as  had  been  assumed  existed,  it  must  diminish  as  the 
square  of  the  distance  from  the  sun ;  otherwise  the 
squares  of  the  periodic  times  of  the  different  planets 
would  not  be  proportional  to  the  cubes  of  the  dis- 
tances, as  Kepler  had  found  them  to  be. 


82        PROBLEM  OF  CENTRAL  FORCES. 

As  early  as  January,  1684,  the  problem  of  central 
forces  was  discussed  by  three  eminent  English  mathe- 
maticians, Sir  Christopher  Wren,  Halley,  and  Hooke  ; 
but  the  discussion  leading  to  no  definite  result, 
Halley,  in  August  of  the  same  year,  went  to  Cam- 
bridge, to  consult  Newton  on  the  subject;  and  without 
mentioning  that  a  discussion  had  been  held,  "  went 
straight  to  the  point,  and  asked  what  would  be  the 
curve  described  by  a  planet  round  the  sun,  on  the 
assumption  that  the  sun's  force  diminished  as  the 
square  of  the  distance."  Newton  replied  promptly, 
"  An  ellipse  ;  "  and  on  being  questioned  by  Halley  as 
to  the  reason  for  his  answer,  he  replied,  "Why,  I  have 
calculated  it."  That  the  calculation  had  been  made 
some  time  previously  is  evident  from  the  further  cir- 
cumstance, we  learn  through  Halley,  that  Newton  could 
not  at  once  put  his  hand  upon  his  former  work ;  but  he 
soon  afterwards  reproduced  it,  and  in  November  sent 
Halley  a  copy  of  the  result.  Soon  after,  Halley  again 
visits  Cambridge  to  confer  with  Newton  about  the 
same  problem,  and  these  conferences  led  to  the  prep- 
aration of  the  "  Principia,"  which  was  published  under 
the  auspices  of  the  Royal  Society,  at  Halley's  own 
charge,  two  years  later.  The  demonstration  of  the 
law  of  gravitation  first  appeared  in  the  "  Principia ;  " 
and  it  is  a  most  noteworthy  fact — which  marks  a  most 
striking  difference  between  the  scientific  activity  of 
those  days  and  the  investigations  of  our  time  —  that 
so  important  a  result,  which  in  all  its  essential  features 
must  have  been  reached  at  least  ten  years  before, 
should  have  been  kept  so  long  by  the  author  to  him- 
self, and  even  by  him  so  far  forgotten  that  he  could 


PROBLEM  OF  CENTRAL  FORCES.        83 


not  at  once  reproduce  one  of  the  chief  steps  in  his 
reasoning. 

The  problem  of  central  forces  as  solved  by  New- 
ton involved,  as  we  have  seen,  two  distinct  questions. 
In  the  first  place,  it  was  necessary  to  determine  the 
rate  according  to  which  the  central  force  varied  with 
the  distance ;  and  Newton  had  shown  that  it  followed 
from  the  third  law  of  Kepler  that  the  force  must 
diminish  with  the  square  of  the  distance;  but  in  this 
he  had  been  to  some  extent  anticipated.  In  the 
second  place,  assuming  a  force  thus  varying,  it  was 
required  to  find  what  would  be  the  character  of  the 
orbit  of  a  body  revolving  round  the  centre  of  force 
under  its  control.  Newton  was  the  first  to  answer 
this  last  question  correctly,  and  he  had  shown,  not 
only  that  the  orbit  would  be  an  ellipse  as  the  first 
law  of  Kepler  required,  but  also  that,  as  the  second 
law  required,  the  radius  vector  must  describe  equal 
areas  in  equal  tinies. 

These  results,  however,  had  been  deductions  drawn 
from  established  principles  of  mechanics  by  the  aid 
of  the  new  calculus.  No  one  thus  far  had  suspected 
the  nature  of  this  central  force ;  and  by  most  scholars 
of  the  period  it  would  have  been  thought  degrading 
to  astronomy  to  associate  the  mechanism  of  the 
heavens  with  the  mechanics  of  the  earth.  The  two 
subjects  were  never  thought  of  in  the  same  connec- 
tions. There  were,  it  is  true,  the  deductions  just  re- 
ferred to,  by  which  it  appeared  that  the  planets 
might  be  sustained  in  their  motions  round  the  sun  by 
the  action  of  a  constant  central  force  controlling  their 
primary  motions.      There  were  also  the  undoubted 


84  LAW   OF   GRAVITATION. 

facts  of  mechanics,  that  weight  was  the  effect  of  a 
direct  pull  or  force  exerted  by  the  earth  on  all  bodies, 
and  that  the  strength  of  this  pull  was  directly  propor- 
tional to  the  amount  of  material  on  which  it  acted. 
As  yet,  however,  these  two  classes  of  facts,  so  closely 
associated  in  our  own  minds,  belonged  to  wholly  dis- 
tinct categories  of  thought,  and  were  no  more  asso- 
ciated than  we  connect  the  fluctuations  of  the  market 
with  the  motions  of  the  moon.  Indeed  that  there 
was  any  intimate  relation  between  force  and  motion 
was  then  a  very  modern  conception. 

The  idea,  that,  after  all,  this  sublime,  inscrutable, 
central  force  of  astronomy  was  simple  commonplace 
gravity  seems  suddenly  to  have  flashed  into  the  mind 
of  Newton.  We  all  know  the  anecdote  of  the  falling 
apple.  The  authority  for  the  story  is  Voltaire,  who 
narrates  it  in  a  somewhat  popular  account  of  New- 
ton's work,  which  he  wrote  for  French  readers  soon 
after  his  return  from  England  in  1.729.  He  gives  as 
his  authority  Catharine  Barton,  a  favorite  niece  of 
Newton.  She  married  Conduit,  a  Fellow  of  the 
Royal  Society  and  one  of  her  uncle's  intimate  friends, 
with  whom  also  Voltaire  was  intimate  during  his  well 
known  residence  in  London  from  1726  to  1729;  and 
it  was  during  this  time,  in  1727,  that  Newton  died. 
The  story  has  been  discredited  by  Sir  David  Brew- 
ster in  his  "Life  of  Newton  ;"  but,  as  must  be  admitted, 
it  is  as  authentic  as  such  a  personal  reminiscence 
could  well  be ;  and  it  is  certain  that  tradition  marked 
the  tree  near  his  mother's  house  at  Woolthorpe  in 
Lincolnshire  as  that  from  which  the  apple  fell,  till 
1 820,  when  owing  to  decay  it  was  cut  down,  and  the 


THE   INDUCTION   OF  NEWTON.  85 


wood  carefully  preserved.  Tradition  also  fixes  the 
date  as  1666,  soon  after  Newton's  graduation  from 
Trinity,  when  he  was  passing  several  months  at  his 
old  home  on  account  of  the  fear  of  the  plague  at 
Cambridge. 

Why  may  not  the  force  which  pulls  the  apple  pull 
the  moon?  We  are  left  in  no  doubt  whatever  in  re- 
gard to  the  general  tenor  of  Newton's  thoughts, 
either  in  the  garden  at  Woolthorpe  or  elsewhere ;  for 
we  are  told  the  story  by  Pemberton  in  the  preface  to 
his  "  View  of  Newton's  Philosophy,"  and  he  had  it 
from  Newton  himself.  If  the  power  of  gravity,  New- 
ton thought,  is  not  sensibly  diminished  at  the  greatest 
heights  to  which  we  can  rise  from  the  earth's  surface, 
neither  at  the  tops  of  the  loftiest  buildings  nor  even 
on  the  summits  of  the  highest  mountains,  why  may  it 
not  extend  much  further  than  is  usually  thought? 
Why  not  as  high  as  the  moon?  If  so,  her  motion 
must  be  influenced  by  it;  perhaps  she  is  retained  in 
her  orbit  thereby. 

This  was  the  simple  thought  suggested,  and  it  was 
this  which  constituted  the  greatest  induction  ever 
made  in  physical  science.  The  moon  is  only  distant 
from  us  some  sixty  times  the  earth's  radius,  and  why 
should  not  the  immense  pull  of  the  earth  on  all  mat- 
ter near  itself  be  felt  at  that  distance?  Of  course  if 
this  is  the  force  which  holds  the  moon  and  the  planets 
to  their  orbits  it  must,  as  can  be  proved  by  Kepler's 
third  law,  diminish  with  the  square  of  the  distance 
from  the  centre  of  motion.  From  the  well  known 
relations  of  the  centre  of  gravity,  the  pull  of  the 
earth  on  all  bodies  near  its  surface,  as  well  as  its  pull 


86  METHOD   OF   CALCULATION. 

on  distant  bodies,  may  be  regarded  as  proceeding 
from  its  centre  of  figure.  Hence  the  force  of  the  pull 
at  the  moon  must  be  as  much  less  than  the  pull  at 
the  earth's  surface  as  the  square  of  sixty-one  is  greater 
than  the  square  of  unity,  that  is,  3721  times  less.  But 
as  the  earth's  pull  is  proportional  to  the  quantity  of 
matter  on  which  it  acts,  so  that  all  bodies  great  or 
small  fall  towards  the  earth  with  the  same  rapidly 
increasing  velocity,  —  the  moon  just  as  fast  and  no 
faster  than  a  stone  under  the  same  conditions, — we 
ought  to  expect  that  the  moon,  at  its  distance,  would 
fall  3721  times  more  slowly  than  a  stone  near  the  sur- 
face. Now  such  a  stone  falls  16  feet  the  first  second, 
and  would  fall  if  it  had  a  chance  57,600  feet  the  first 
minute ;  so  that  the  moon  should  fall  about  fifteen 
and  a  half  feet  during  the  first  minute  of  time.  But 
how  much  does  the  moon  fall?  This  is  the  next 
question  which  Newton  asked  ;  and  it  is  by  no  means 
so  easily  answered  as  the  one  we  have  just  solved  so 
readily. 

If  the  moon  and  planets  have  the  compound  mo- 
tion which  Newton  assigned  to  them,  they  are  in  the 
paradoxical  condition  of  beginning  to  fall  at  every 
moment  of  time  towards  their  primaries;  always  be- 
ginning to  fall  but  never  falling.  Should  the  earth's 
pull  at  any  instant  suddenly  cease  the  moon  would  at 
once  resume  its  primary  motion  of  translation,  start- 
ing off  on  a  tangent  with  the  uniform  velocity  which 
it  had  at  that  moment  in  its  orbit.  If  now  we  con- 
struct in  imagination  an  arc  of  the  moon's  orbit  de- 
scribed around  a  centre  representing  the  earth,  with 
a  tangent  starting  off  at  the  point  where  the  earth's 


FIRST  RESULT  UNSATISFACTORY.       87 

pull  is  assumed  to  stop ;  and  from  this  point  of  con- 
tact measure  off  the  distance  on  the  arc  over  which 
the  moon  actually  moves  in  one  minute ;  and  finally 
through  the  extremity  of  the  arc  thus  found  draw 
from  the  centre  a  radius,  and  extend  the  line  until  it 
intersects  the  tangent,  —  then  this  intersection  will  be 
the  point  which  the  moon  would  have  reached  in  one 
minute  had  it  started  off  on  the  tangent  as  assumed ; 
and  the  portion  of  the  radius  between  the  tangent  and 
the  arc  will  represent  the  distance  through  which  the 
moon  actually  falls  to  the  earth  during  this  same 
minute  of  time.  Knowing  the  radius  of  the  orbit 
and  the  angle  subtended  by  the  arc  at  the  centre, 
and  assuming  —  as  we  may  —  that  such  a  small  arc 
is  practically  circular,  it  would  be  the  simplest  of 
trigonometrical  problems  to  calculate  the  distance  in 
question.  In  Newton's  time,  however,  the  calcula- 
tion involved  many  uncertain  elements,  which  he 
showed  great  judgment  in  selecting  and  skill  in  com- 
bining. But  the  first  result  was  unsatisfactory,  for  it 
appeared  that  the  fall  was  only  thirteen  feet,  instead 
of  fifteen  and  one  half  feet  as  the  theory  required. 

Most  men  would  have  regarded  this  as  at  least  a 
sufficient  approximation  to  induce  them  to  continue 
the  investigation ;  and  no  circumstance  indicates 
more  plainly  the  balance  of  Newton's  mind  and  the 
dispassionateness  of  his  temperament  than  that  he  re- 
garded the  result  as  disproof,  and  at  once  dismissed 
the  theory  from  his  thoughts. 

In  a  few  years,  however,  the  cause  of  this  failure 
to  verify  the  theory  was  fully  explained.  The  cal- 
culation which  Newton  had  made  involved  a  know- 

7 


88  THE  THEORY  VERIFIED. 

ledge  of  the  moon's  distance  in  feet,  while  the 
astronomical  determination  of  this  distance  depended 
on  trigonometrical  measurements  of  which  the  earth's 
radius  was  the  base ;  and  only  gave  the  information 
that  the  distance  was  about  sixty-one  times  this  ra- 
dius. To  reduce  the  result  to  feet,  it  was  necessary 
to  know  the  length  of  the  earth's  radius  in  feet,  and 
here  was  the  difficulty.  We  cannot  of  course  meas- 
ure the  radius  directly,  but  we  can  measure  an  arc 
of  a  meridian  circle  on  the  earth's  surface,  and  from 
the  length  of  an  arc  of  known  extent  —  say  five  de- 
grees—  calculate  the  length  of  the  radius.  This  is  what 
Newton  had  done,  assuming,  according  to  the  received 
estimate  at  the  time,  that  one  degree  on  the  meridian 
measured  sixty  miles.  In  167 1,  however,  a  new 
measurement  of  an  arc  of  a  meridian,  between  Ami- 
ens and  Malvoisine  in  France,  was  made  by  the 
astronomer  Picard,  which  showed  that  the  received 
length  of  a  degree  was  greatly  in  error;  and  that 
instead  of  being  sixty  it  was  sixty-nine  English  stat- 
ute miles  of  5280  feet  each.  When  this  result  be- 
came accredited  in  England,  Newton  revised  the 
calculation  which  had  so  long  been  laid  aside  ;  and 
the  result  was  an  agreement  with  theory  so  exact  as 
to  leave  no  longer  any  doubt  in  his  mind  of  the  truth 
of  his  early  conception.  As  the  story  is  told  by 
Robinson,  "  He  went  home,  took  out  his  old  papers, 
and  resumed  his  calculations.  As  they  drew  to  a 
close  he  was  so  much  agitated  that  he  was  obliged 
to  desire  a  friend  to  finish  them." 

This  in  outline  is  the  history  of  the  greatest  scien- 
tific induction  which  man  has  ever  made.     In  draw- 


THE   INDUCTION   OF  NEWTON.  89 


ing  the  sketch,  I  have  given  prominence  to  those 
features  which  from  my  point  of  view  seemed  most 
essential,  and  have  doubtless  passed  unnoticed  facts 
and  relations  which  others  might  deem  more  impor- 
tant. But  the  interaction  of  mind  on  mind,  which 
scientific  progress  involves,  is  usually  very  complex  ; 
and,  in  the  absence  of  detailed  information,  there  is 
room  for  great  differences  of  opinion.  It  is  much  to 
be  regretted  that  we  have  not  fuller  knowledge,  espe- 
cially in  regard  to  the  sequence  in  which  the  various 
elements  of  the  problem  were  presented  to  Newton's 
mind  ;  but  he,  unlike  his  predecessor  Kepler,  was  very 
reticent,  and  did  not  display  all  the  processes  of  his 
thoughts. 

We  might,  with  Whewell,  classify  the  general  results 
of  Newton's  work  under  five  different  propositions, 
which  undoubtedly  came  before  him  at  one  time 
or  another  as  separate  problems:  first,  that  the 
strength  of  the  pull  of  the  sun  on  different  planets 
diminishes  with  the  square  of  the  distance;  secondly, 
that  a  force  so  acting  would  cause  the  planet  to 
move  in  elliptical  orbits,  in  accordance  with  the  first 
and  second  laws  of  Kepler;  thirdly,  that  the  earth 
so  acts  on  the  moon,  and  that  this  force  is  identical 
with  gravity;  fourthly,  that  this  force  is  universal, 
causing  an  attraction  between  all  bodies  under  all 
conditions ;  fifthly,  that  the  strength  of  the  force 
increases  in  the  same  proportion  as  the  combined 
weights  of  the  attracting  bodies,  and  may  be  re- 
garded as  the  sum  of  the  actions  of  the  various  par- 
ticles or  units  of  mass  of  which  they  consist. 

Such  a  classification   is   useful,  as  a  summary  of 


90  THE   INDUCTION   OF   NEWTON. 

what  has  been  —  in  great  measure  —  already  stated, 
as  pointing  out  the  separate  elements  of  the  problem, 
and  as  showing  how  great  the  work  really  was.  But 
all  these  propositions  except  the  third,  were  deduc- 
tions from  known  principles ;  and  the  identity  of  the 
central  force  with  gravity  being  granted,  the  rest 
necessarily  followed.  Not  that  we  would  in  the  least 
degree  depreciate  the  skill  with  which  these  deduc- 
tions were  worked  out.  On  the  contrary,  as  with 
every  investigation,  this  was  Newton's  real  work  ;  "  hie 
labor,  hoc  opus  est;"  and  it  has  always  won,  and  ever 
will  claim  the  admiration  of  the  world.  But  it  was 
the  great  induction,  and  not  these  deductions  which 
we  are  endeavoring  to  illustrate.  The  induction  was 
to  a  large  extent  —  if  not  wholly  —  a  spontaneous 
action  of  the  mind ;  but  it  is  by  just  such  action  that 
the  level  of  knowledge  is  raised.  After  any  great 
induction  it  always  requires  time  —  it  may  be  long 
time  —  to  work  up  to  the  new  level.  It  was  so  after 
Hipparchus ;  it  was  so  after  Copernicus ;  it  was  so 
after  Kepler ;  and  astronomy  has  not  yet  reached  the 
level  which  Newton  set.  The  deductions  may  require 
greater  intellectual  skill,  as  they  necessarily  involve 
incomparably  greater  labor;  but  they  do  not  raise 
the  level.  As  in  building,  it  requires  little  work  to 
raise  the  scaffolding,  but  then  comes  the  long  and 
arduous  toil  of  the  builders  to  prepare  the  walls  on 
which  to  mount  still  higher. 

If  gravity  reaches  to  the  tops  of  the  highest  moun- 
tains, why  not  as  high  as  the  moon  ?  This  was  the 
fundamental  conception  which  led  to  the  great  result. 
Seeing  how  apparently  trivial  and  accidental  was  the 


THE   INDUCTION   OF  NEWTON.  9 1 


thought  which  bound  together  the  universe  in  its  all 
embracing  grasp,  some  may  imagine  that  the  individ- 
ual merit  of  the  conception  was  inconsiderable.  But 
they  must  remember  that  the  thought  would  have  been 
barren  without  the  knowledge  to  make  it  pregnant, 
or  without  the  labor  to  make  it  real.  Others,  like 
Hooke  and  Cassini,  did  claim  to  have  had  the  thought 
as  well  as  Newton  ;  but  their  thought  was  barren,  and 
the  world  has  paid  no  regard  to  their  claims.  Again, 
some  may  think  that,  given  the  knowledge  and  the 
intellectual  power,  the  thought  came  without  observa- 
tion, and  that  to  God  and  not  to  man  belongs  all  the 
glory.  If  by  this  is  meant  that  the  thought  came  as 
an  inspiration  to  a  mind  prepared  to  receive  it,  I 
should  agree  to  the  proposition; 

"  For  merit  lives  from  man  to  man, 
And  not  from  man,  O  Lord,  to  Thee." 

And  I  myself  believe  that  just  as  to  the  intellectually 
strong  and  teachable  there  come  revelations  of  larger 
knowledge  about  material  things,  so  to  the  spiritually 
minded  and  open-hearted  there  comes  in  a  similar 
way  a  deeper  insight  into  the  spiritual  life;  and  it  is 
because  I  believe  these  material  relations  to  be  a 
type  of  the  spiritual,  and  to  have  the  same,  though 
no  more  certain  sanctions,  and  it  is  because  I  hope, 
through  a  more  intimate  knowledge  of  the  facts,  to 
aid  in  reconciling  the  two  orders  of  truth,  that  I  have 
dwelt  so  long  on  this  instructive  history. 

The  character  of  Newton  was  entirely  in  harmony 
with  his  lofty  career.  It  was  marked  by  sedateness 
of  demeanor;  soberness  of  conversation;  sobriety  of 


92        THE  CHARACTER  OF  NEWTON. 

conduct;  persistency  in  effort;  devotion  of  will;  hu- 
mility of  disposition  ;  reverence  of  mind,  and  absorp- 
tion in  thought.  He  never  would  admit  there  was 
any  difference  between  himself  and  other  men ;  and 
when  asked  how  he  made  his  discoveries,  replied,  "  I 
keep  the  subject  of  my  inquiry  constantly  before  me, 
and  wait  till  the  first  dawning  opens  gradually,  by 
little  and  little,  into  a  full  and  clear  light."  It  is  into 
minds  in  such  a  frame  that  the  light  shines ;  and  by 
waiting  on  the  Eternal  Purpose  the  revelations  of 
great  truths  come. 


INDUCTION  RAISES  THE  LEVEL  OF  KNOWLEDGE.      93 


LECTURE    IV. 

DEDUCTION. 

IN  my  last  lecture  I  said  that  a  new  induction  raises 
the  level  of  human  knowledge;  and  this  figura- 
tive expression  very  exactly  indicates  the  new  rela- 
tions which  are  thus  introduced  into  the  world  of 
thought.  There  is  not  simply  an  addition  to  knowl- 
edge, but  the  old  knowledge  is  seen  in  a  new  light. 
Facts  previously  disconnected  are  found  to  be  united 
by  common  bonds.  Phenomena  which  appeared 
mysterious  and  fortuitous  now  appear  regular  and 
natural.  Principles  which  were  supposed  to  be  fun- 
damental are  found  to  be  dependent.  Partial  and 
formal  laws  are  merged  in  more  universal  and  sim- 
pler modes  of  action.  Order  and  harmony  prevail 
where  before  was  only  confusion  and  discord. 

But  to  show  what  are  the  results  of  the  new  princi- 
ple that  has  been  introduced,  to  trace  all  its  connec- 
tions, to  develop  the  consequences,  both  near  and 
remote,  to  test  by  observation  or  experiment,  the 
deductions  in  every  detail,  and  to  follow  out  the 
lines  of  investigation  thus  opened,  requires  a  great 
amount  of  thought  and  labor,  and  the  more  in  pro- 
portion as  the  previous  induction  is  broader  and 
more  commanding.     In  this  way  the  general  standard 


94  DEDUCTION  BROADENS   KNOWLEDGE. 

of  knowledge  is  brought  up  to  the  new  level,  and  the 
foundations  are  laid  on  which  to  rise  to  a  still  more 
commanding  position.  It  is  work  of  this  sort  which 
almost  exclusively  occupies  the  time  and  taxes  the 
energies  of  the  great  body  of  scientific  investigators ; 
and  in  the  economy  of  nature  many  thousand  workers 
are  ready  to  carry  out  the  conceptions  of  one  great 
master. 

The  great  originator  is  highly  favored  among  men, 
but  let  it  not  be  inferred  that  the  part  of  his  fellow- 
workers  is  less  honorable,  or  their  labor  less  difficult, 
or  less  necessary.     Not  only  is  it  that 

"All  are  architects  of  Fate, 

Building  on  these  walls  of  time," 

but  it  is  also  true  that  some  of  the  greatest  intellect- 
ual achievements  have  consisted  wholly  in  following 
out  well-established  principles  to  their  necessary  con- 
sequences. Newton's  great  induction  commands  our 
highest  admiration,  but  so  do  equally  the  deductions 
which  Laplace  and  Lagrange  and  Gauss  severally 
drew  from  Newton's  all-embracing  law.  No  work 
of  science  can  be  compared  with  the  "  Principia  "  in 
the  effect  produced  on  the  progress  of  knowledge; 
but  it  may  be  questioned  whether  it  shows  as  great 
intellectual  power  as  the  "  Mecanique  Celeste." 

The  mathematical  sciences  give  us  the  most  char- 
acteristic examples  of  the  deductive  method,  and 
mathematics  is  the  most  important  tool  in  such  pro- 
cesses of  thought.  The  necessity  of  such  aid  arises 
from  the  limited  power  of  the  human  mind  in  com- 
bining details,  in  following  sequences,  in  remember- 


ARABIC   NUMBERS.  95 


ing  successive  steps,  and  in  general  in  concentrating 
thought.  The  various  forms  of  calculus  help  the  rea- 
soning powers  very  much  in  the  same  way  that  the 
microscope,  the  telescope,  or  the  telephone,  aid  the 
eye  or  the  ear  in  observing  natural  phenomena. 

This  fact  we  recognize  in  the  simplest  forms  of 
mathematical  calculation.  The  Arabic  numerals, 
with  the  so-called  decimal  system  of  arithmetic,  en- 
able any  one  readily  to  obtain  results  which,  without 
their  aid,  would  be  attainable  only  by  a  mathematical 
genius;  and  if  we  analyze  the  mental  processes  of 
the  remarkable  calculators  who  from  time  to  time 
appear,  we  find  that  their  wonderful  ability  depends 
chiefly  on  a  vividness  of  memory  and  imagination, 
which  enables  them  to  keep  before  their  minds,  and 
thus  combine,  a  great  number  of  partial  results. 
Each  of  these  by  itself  might  have  been  obtained 
mentally  by  the  average  man ;  but  he  finds  it  neces- 
sary to  aid  his  memory  by  noting  down  every  step 
of  his  calculation  on  slate  or  paper. 

Men  with  such  a  knack  at  figures  are  also  able 
to  combine  results  by  quick  methods  which  are  out 
of  the  reach  of  ordinary  computers;  while  the  com- 
mon rules  of  decimal  arithmetic  are  adapted  to  the 
average  mind,  and  give  just  the  aid  which  will  enable 
it  to  reach  most  rapidly  and  accurately,  the  required 
result. 

It  may  be  well  here  to  set  right  a  common  mis- 
apprehension, that  the  rules  of  arithmetic  have  some 
special  relation  to  the  number  ten.  Since  Nature 
gave  man  ten  "fingers  or  digits,  which  make  a  very 
simple  but   efficient   calculating  engine,   he    instinc- 


96  DECIMAL   SYSTEM. 

tively,  at  a  very  early  period,  distinguished  and  gave 
names  to  ten  corresponding  numerals,  also  frequently 
called  digits;  but  it  was  not  until  man  had  tried  vari- 
ous clumsy  expedients  of  combining  these  digits  to 
express  larger  numbers,  that  some  good  genius,  sup- 
posed to  have  been  an  Arabian,  devised  our  simple 
method  of  expressing  numerical  values.  The  arith- 
metical rules  are  the  outcome  of  this  method,  and 
would  work  just  as  well  with  any  other  number  of 
digits  as  with  ten.  Eight  digits  would  have  given  us 
a  simpler  arithmetic,  and  twelve  digits,  in  many  re- 
spects, a  more  convenient  one.  Such,  however,  is 
the  force  of  habit  and  the  conservatism  of  education 
that  a  change  now  would  probably  be  impracticable ; 
but  we  cannot  but  regret  that  our  early  parents  did 
not  omit  the  thumbs  in  the  first  count.  Eight  units 
can  be  evenly  divided  three  times,  ten  units  but  once; 
and  this  power  of  successive  subdivision  is  of  para- 
mount importance  in  commercial  transactions,  as  the 
experience  in  France  with  decimal  weights  and 
measures  plainly  shows.1 

1  The  truth  of  this  statement,  although  really  so  simple, 
seems  so  inconsistent  with  our  familiar  habits  and  ordinary 
experience,  that  some  further  illustrations  of  it  may  be  desired. 
In  our  system  of  enumeration  we  use  in  addition  to  the  zero 
mark  separate  signs  for  the  first  nine  digits,  and  express  all 
higher  numbers  by  an  ingenious  method  of  combining  these 
signs,  or  figures,  as  the  signs  are  called.  The  system  consists 
in  writing  the  figures  in  a  definite  order  on  a  horizontal  line, 
and  assigning  to  the  digits  a  value  increasing  by  powers  of  ten 
as  we  proceed  from  right  to  left.  The  figure  in  the  first  or 
units'  place  stands  for  single  digits  ;  the  figure  in  the  second  or 
tens'  place  stands  for  ten  times  the  number  indicated  by  the 


OCTUPLE   SYSTEM.  97 

The  French  system  of  weights  and  measures  is 
constantly  advocated  on  account  of  its  decimal  sub- 
division, but  these  are  a  positive  disadvantage.  The 
one  valuable  feature  of  the  French  system  is  the 
simple  relation  which  it  establishes  between  measures 
and  weights,  and  it  would  doubtless  be  a  great  gain 
if  such  a  system  were  adopted  by  all  nations ;  but  it 
would  be  a  still  greater  gain  if  we  could  get  rid  of 

sign ;  the  figure  in  the  third  or  hundreds'  place  for  ten  times 
ten,  or  one  hundred  times,  the  number  indicated  ;  that  in  the 
fourth  or  thousandths'  place  for  ten  times  ten  times  ten,  or  one 
thousand  times,  the  number  expressed  ;  and  so  on.  The  ex- 
pression 63,597,  for  example,  signifies  six  ten  thousand,  added 
to  three  thousand,  added  to  five  hundred,  added  to  nine  tens, 
added  to  seven  ;  and  we  are  so  familiar  with  this  method  of 
enumeration  that  we  are  apt  to  forget  how  artificial  it  is,  and 
how  much  we  are  indebted  to  the  ingenious  men  of  Arabia,  or 
elsewhere  in  the  East,  who  invented  the  system. 

The  efficiency  of  this  system,  and  the  validity  of  the  rules 
which  arise  under  it,  depend  not  on  any  peculiar  virtue  in  the 
number  ten,  but  simply  on  the  mode  of  combining  the  figures 
to  express  values.  As  above  said,  there  was  no  reason  for 
selecting  the  number  ten  more  weighty  than  the  authority  of 
the  ten  of  fingers  and  the  ten  of  toes  ;  and  any  other  number 
might  have  been  taken  as  the  basis  of  the  system  equally  well. 
For  example,  we  might  use  eight  as  the  basis  of  the  system,  and 
assign  to  the  digits,  arranged  as  before,  values  increasing  by 
powers  of  eight.  We  should  then  discard  two  of  our  figures,  8 
and  9,  and  omit  the  corresponding  names  in  counting,  thus :  — 


I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Sec. 

Decimals 

I 

2 

3 

4 

5 

6 

7 

10 

11 

12 

Sec. 

Octuples. 

We  might  use  the  same  names  and  figures  for  all  the  numbers 
up  to  seven  ;  but  we  should  be  obliged  to  give  a  wholly  different 
significance  to  all  compound  numbers,  while  assigning  to  them 


98  OCTUPLE   SYSTEM. 

two  of  our  digits,  and  establish  our  system  of  arith- 
metic   on    an   octonary  instead   of  a  decimal   basis. 

the  names  we  use  for  the  corresponding;  compounds  (not  the 
corresponding  numbers)  on  the  decimal  system.  Thus  ten 
(10)  in  the  octuples  would  have  the  same  value  as  eight  (8)  in 
the  decimals  ;  twenty  in  the  octuples  the  same  value  as  sixteen 
in  the  decimals;  one  hundred  in  the  octuples  the  same  value 
as  eight  times  eight,  or  sixty-four,  in  the  decimals,  &c.  How 
completely  the  introduction  of  a  new  system  would  destroy  our 
association  with  numbers  will  be  evident  from  the  following 
multiplication  table  on  the  octonary  system :  — 

MULTIPLICATION  TABLE. 
Octonary  System. 


I 

2 

3 

4 

5 

6 

7 

10 

2 

4 

6 

10 

12 

14 

16 

20 

3 

6 

ii 

14 

17 

22 

25 

30 

4 

10 

14 

20 

24 

30 

34 

40 

5 

12 

17 

24 

3i 

36 

43 

50 

6 

14 

22 

30 

36 

44 

5- 

60 

7 

16 

25 

34 

43 

52 

61 

70 

10 

20 

3° 

40 

50 

60 

70 

100 

Obviously,  it  would  be  impracticable  for  us  who  learned  to 
cipher  by  the  decimal  system  to  change  our  habits  of  thought, 
and  acquire  a  second  nature  under  which  twice  four  would  sug- 
gest involuntarily  ten,  or  four  times  six  thirty,  with  correspond- 
ing changes  in  all  processes  of  simple  addition  and  subtraction. 
Think  of  the  confusion  of  bank  clerks  and  other  lightning  cal- 
culators if  six  and  seven  became  fifteen,  or  three  from  ten  five  ! 
Nevertheless,  apart  from  the  force  of  habit  the  transition  would 
be  a  very  simple  one.  The  fundamental  operations  of  arithme- 
tic would  not  be  essentially  altered  thereby ;  and  to  those  edu- 
cated in  it  the  octuple  system  would  appear  as  natural  as  the 
one  we  so  familiarly  employ.  A  single  example  will  make  this 
point  clear. 

Let  us  assume  that  we  have  two  numbers  234  and  345  writ- 
ten on  the  octuple  system  to  multiply  together.     We  proceed 


OCTUPLE   SYSTEM.  99 

Although  this  digression  has  no  immediate  bearing 
on  our  subject,  it  shows  how  conventional  our  system 

exactly  as  we  should  on  the  decimal  system  only  using  the  new 
multiplication  table,  and  making  the  corresponding  additions, 
thus :  — 

234  156 

345  _  229 

1414  1404 

1 160  312 

l-\  312 


i°5>6x4  35-7-4 

We  read  the  two  numbers  two  hundred  and  thirty  four  and 
three  hundred  and  forty-five,  and  the  product  one  hundred  and 
five  thousand  six  hundred  and  fourteen  just  as  we  should  on 
the  decimal  system.  But  on  the  octuple  system  the  same  num- 
bers express  wholly  different  values.  These  values,  however, 
can  be  readily  reduced  to  the  decimal  basis,  if  we  remember 
that  on  this  basis  the  value  of  the  successive  places  in  the  oc- 
tuple enumeration  increase  by  powers  of  eight.  Hence,  the 
value  of  234  in  octuples  would  be  found  in  decimals  thus  :  — 


Octuples. 

D 

ecimals. 

200  = 

2 

X  8 

X  8 

=3 

I2S 

30  = 

3 

X  8 

= 

24 

4  = 

= 

4 

234  156 

So  also  the  value  of  345  in  octuples  would  be  found  :  — 

300  =  3  X  8  X  8  =  192 

40  =  4  X  8  =32 

5  =  =_5 

345  229 

The  product  of  156  by  229  decimals  has  already  been  found 
above  to  be  35,724,  and  we  can  now  prove  that  the  ordinary  rule 
of  multiplication  applies  to  octuples  as  well  as  to  decimals,  by 


100  MATHEMATICS   AIDS   DEDUCTION. 

of  arithmetic  really  is,  and  what  an  efficient  aid  it  is 
in  our  mental  processes. 

As  we  go  forward  in  the  study  of  mathematical 
subjects  the  more  necessary  does  the  aid  furnished 
by  mathematical  symbols  become,  and  we  very  soon 
reach  a  point  where  even  the  most  gifted  intellect 
cannot  dispense  with  their  arbitrary  forms.  They 
enable  the  mind  to  combine  conditions  and  see  rela- 
tions which  otherwise  it  could  not  possibly  grasp. 
Hence  it  is  that  every  great  improvement  in  math- 
ematical methods  has  always  been  followed  by  a 
great  extension  in  our  knowledge  of  material  re- 
lations; new  deductions  from  old  principles  have 
become  possible,  and  thus  knowledge  has  been  broad- 
ened and  the  way  made  ready  for  larger  inductions. 

showing  that  this  product  is  the  exact  equivalent  of  the  octuple 
product  105,614  also  before  obtained  by  following  the  regular 
arithmetical  rule,  of  course  using  the  octuple  multiplication 
table  and  the  corresponding  octuple  additions  as  before  de- 
scribed. 

Octuples.  Decimals. 

100000  =  iX8X8XSX8X8  =  32768 

5000  =  5x8x8x8  =    2560 

600  =  6X8X8  =384 

10  =  1  X  8  =8 

4  =  =4 


105,614=  =35.724 

The  same  point  could  be  illustrated  by  other  arithmetical  oper- 
ations ;  but  the  above  example  is  sufficient  to  enforce  the  state- 
ment made  above  ;  and  it  must  now  be  evident  that  the  great 
merit  of  what  we  wrongly  call  "decimal"  arithmetic  depends  on 
the  system  of  Arabic  numerals,  and  not  at  all  on  the  number  of 
digits  it  employs. 


SCIENCE   OF   QUANTITATIVE   RELATIONS.        IOI 


It  was  so  when  the  Cartesian  geometry  gave  a  knowl- 
edge of  the  properties  and  relations  of  curved  lines 
and  surfaces  before  unsuspected.  It  was  so  when 
Newton  and  Leibnitz  invented  general  methods  of 
dealing  with  the  so-called  infinitesimal  quantities  of 
algebra  and  geometry,  which  led  at  once  to  the  suc- 
cessful solution  of  the  problem  of  central  forces.  It 
was  so  again,  after  Newton's  death,  when  the  conse- 
quences of  the  law  of  gravitation  were  developed  in 
proportion  as  the  resources  of  the  new  calculus  were 
enlarged  by  the  great  mathematicians  of  the  eight- 
eenth century,  — such  men  as  Euler,  Laplace,  and 
Lagrange. 

Mathematics,  however,  is  a  great  deal  more  than 
an  instrument  for  deductive  reasoning.     Just  as  logic 
has  loftier  aims  than  merely  to  dissect  arguments  and 
to  lay  bare  their  syllogistic  forms  and  becomes  in  its 
larger  expressions  the  science  of  thought,  so  math- 
ematics is  the  science  of  quantitative  relations  wholly 
independent  of  their  material  expressions;    and  the 
so-called  multiple  algebra  of  our  own  day  has  been 
developed  far  beyond  our  positive  knowledge  of  ma- 
terial relations,  and  it  is  at  this  moment  waiting  for 
some  higher  induction  or  broader  generalization  to 
open  new  worlds  to  conquer.     Indeed,  so  transcen- 
dental are  the  abstractions  involved  that  few  educated 
men,  not  mathematical  specialists,  are  able  to  follow 
them;   although  in  some  curious  works  of  fiction  at- 
tempts have  been  made  to  show  the  possibilities  of 
conceiving  of  extension  in  more  than  three  dimen- 
sions.    In  less  abstract  relations,  on  the  other  hand, 
mathematical  analysis  has  not  yet  satisfied  the  de- 


102       SYMBOLICAL   LANGUAGE   OF   CHEMISTRY. 

mands  of  existing  physical  problems ;  and  more 
satisfactory  and  exhaustive  methods  of  solving  equa- 
tions of  higher  degrees  would  enable  the  physicists 
to  broaden  their  deductions  in  many  directions. 

To  a  limited  extent  the  symbolical  language  of 
chemistry  may  be  used  like  mathematical  formulae, 
and  has  a  similar  value  in  facilitating  deduction. 
But  its  terms  have  a  far  more  restricted  meaning, 
and  are  therefore  less  general ;  and  moreover,  the 
chemical  formulae,  which  we  call  reactions,  only  ex- 
press the  very  simple  relations  of  combination  and 
decomposition. 

As  the  use  of  the  symbolical  notation  of  chemistry 
is  for  the  most  part  restricted  to  chemical  students,  a 
brief  description  of  the  system  may  be  necessary  in 
order  to  render  the  statement  just  made  generally 
intelligible. 

We  recognize  at  the  present  time  about  seventy 
well-defined  elementary  substances,  and  in  addition 
to  these  there  are  several  others  whose  authenticity 
has  not  yet  been  satisfactorily  established.  From 
these  elementary  substances  all  known  materials  can 
be  formed ;  and  into  these  the  various  substances 
which  exist  on  the  surface  of  the  earth  can  be  re- 
solved by  processes  with  which  all  chemists  are 
familiar.  Moreover,  when  these  elementary  sub- 
stances unite  to  form  compound  bodies,  the  combi- 
nation takes  place  in  certain  definite  proportions  by 
weight. 

The  modern  theory  of  chemistry,  which  we  shall 
have  occasion  to  discuss  more  at  length  hereafter, 
assumes  that  each  elementary  substance  is  an  aggre- 


THE   "ATOMS'"   OF   CHEMISTRY.  103 


gate  of  exceedingly  minute  particles,  called  atoms, 
which  are  indivisible  by  any  chemical  means  now 
known,  and  which  are  alike  in  every  respect.  Thus 
a  mass  of  the  elementary  substance  sulphur  is  an 
aggregate  of  atoms,  all  of  which  are  exactly  alike, 
but  wholly  different  from  the  atoms  of  any  other 
elementary  substance.  These  atoms,  being  definite 
masses  of  matter,  must  have  definite  weights ;  all  the 
atoms  of  sulphur,  for  example,  absolutely  the  same 
weight,  but  a  very  different  weight  from  that  of  the 
atoms  of  iron  or  from  that  of  the  atoms  of  oxygen, 
two  other  elementary  substances. 

If  the  mental  concepts  we  call  atoms  are  really 
entities,  they  must  have  a  degree  of  minuteness 
which  vastly  surpasses  our  powers  of  observation. 
Granting  the  existence  of  such  minute  particles,  there 
are  known  facts  of  physics  and  chemistry  which  com- 
pel us  to  assign  limits  to  their  magnitude  on  either 
side ;  and  Sir  William  Thomson  has  estimated  that  if 
a  drop  of  water  were  magnified  to  the  size  of  the 
world,  the  atoms  of  which  it  consists  would  certainly 
appear  larger  than  boys'  marbles,  and  with  equal 
certainty  smaller  than  cricket  balls.  The  almost  in- 
conceivable minuteness  of  the  assumed  atoms  is, 
however,  in  itself  no  weighty  argument  against  the 
atomic  theory ;  for  in  a  universe  in  which  we  recog- 
nize the  infinitely  great,  why  should  we  not  expect  to 
find  also  the  infinitely  small?  If  there  be  a  macro- 
cosmos  around  us,  why  should  not  there  be  also  a 
microcosmos?  And  if  creation  be  not  limited  by  the 
powers  of  the  telescope,  why  should  it  be  limited  by 
the  powers  of  the   microscope?     The  proof  of  the 


104  ATOMS   AND   MOLECULES. 

existence  of  atoms  is  solely  a  question  of  sufficient 
evidence,  and  may  be  reached  in  time ;  but  as  yet 
they  can  only  be  regarded  as  postulates  of  our  scien- 
tific systems,  the  ultimate  material  units  out  of  which 
the  mind  seeks  to  construct  masses  of  matter.  To 
our  crude  conceptions  they  are  the  bricks,  as  it  were, 
of  the  material  universe. 

According  to  the  atomic  theory,  when  elementary 
substances  combine,  the  union  takes  place  between 
the  atoms;  and  the  groups  of  atoms  thus  formed  are 
called  molecules,  and  only  like  molecules  aggregate 
together  to  form  masses  of  different  substances.  Thus 
when  oxygen  gas  unites  with  hydrogen  gas  to  form 
water,  one  atom  of  oxygen  unites  with  two  atoms 
of  hydrogen  to  form  one  molecule  of  water;  and  a 
drop  of  water  is  simply  an  aggregate  of  molecules 
of  this  kind,  so  numerous  that  they  can  only  be 
counted  when  all  the  sands  of  the  earth  have  been 
numbered  ;  but  all  these  molecules  are  exactly  alike, 
each  consisting  of  two  atoms  of  hydrogen  and  one 
of  oxygen. 

If  the  atoms  have  definite  weights,  such  a  combi- 
nation as  we  have  just  described  must  take  place  in 
the  definite  proportions  of  these  weights.  As  the 
combined  weight  of  two  atoms  of  hydrogen  is  to  the 
weight  of  one  atom  of  oxygen,  so  and  in  just  this 
proportion  by  weight  must  hydrogen  gas  combine 
with  oxygen  gas  to  form  water ;  and  the  same  gen- 
eral principle  must  hold  in  the  combination  of  all 
other  atoms,  and  in  the  production  of  all  other  com- 
pounds. Hence,  according  to  the  atomic  theory,  the 
combining  proportions  of  chemistry  are  simply  the 


COMBINING   PROPORTIONS   OF  CHEMISTRY.       105 

relative  weights  of  the  atoms.  Obviously,  then,  we 
can  infer  from  the  combining  weights  of  the  ele- 
mentary substances,  which  can  be  accurately  ob- 
served, the  relative  weights  of  those  abstract  units 
we  call  atoms;  and  in  our  modern  chemistry  the 
combining  proportions  of  the  elementary  substances 
are  called,  under  certain  limitations,  the  atomic 
weights  of  the  chemical  elements.  The  smallest  of 
these  weights  is  the  weight  of  the  atom  of  hydrogen, 
which  we  take  as  the  unit  of  the  system.  The  atom 
of  oxygen  weighs  sixteen  of  these  units;  the  atom  of 
sulphur  thirty-two ;  and  the  atom  of  iron  fifty-six  of 
the  same  units.  In  general,  the  atomic  weight  of  an 
elementary  substance  indicates  how  many  times  the 
atoms  of  which  it  consists  weigh  more  than  the 
atoms  of  hydrogen. 

And  here  it  must  not  be  forgotten  that  although 
the  atoms  are  wholly  theoretical  concepts,  these  rela- 
tive weights  are  definite  facts  of  observation ;  and,  as 
already  stated,  are  deduced  directly  from  the  definite 
proportions  in  which  the  elementary  substances  are 
known  to  combine.  These  values  are  independent 
of  the  atomic  theory ;  but  we  can  most  easily  make 
the  facts  intelligible  in  the  terms  of  this  theory,  for 
the  theory  gives  to  the  phenomena  a  concrete  expres- 
sion, and  thus  enables  us  to  relate  them  to  the  rest  of 
our  knowledge. 

If  we  know  the  number  of  atoms  of  each  kind 
which  enter  into  the  composition  of  a  molecule  of 
any  substance,  we  can  find  the  weight  of  that  mole- 
cule by  simply  adding  the  weights  of  the  several 
atoms.     Thus  a  molecule  of  water,  consisting  of  one 


106  EXAMPLES   OF   CHEMICAL   SYMBOLS. 

atom  of  oxygen  and  two  atoms  of  hydrogen,  must 
weigh  16  +  2  =  18. 

Now  it  will  be  obvious  that  if  we  arbitrarily  select 
a  symbol  to  stand  for  an  atom  of  each  element,  we 
can  readily  represent  the  molecule  of  any  substance 
whose  composition  is  known,  by  simply  writing  to- 
gether these  symbols  like  letters  in  a  word. 

In  our  text-books  of  chemistry  you  will  find  a  table 
giving,  after  the  name  of  each  elementary  substance, 
the  symbol  which  has  been  selected  to  represent  its 
atom,  and  also  the  value  of  the  atomic  weight.  Thus 
the  atom  of  hydrogen  is  represented  by  H ;  and  its 
atomic  weight,  as  we  have  said,  is  the  unit  of  the  sys- 
tem. The  atom  of  oxygen  is  represented  by  O,  and 
its  atomic  weight  is  16.  The  atom  of  carbon  is  rep- 
resented by  C,  and  its  atomic  weight  is  12.  The  atom 
of  nitrogen  is  represented  by  N,  and  its  atomic  weight 
is  14. 

We  represent,  then,  a  molecule  of  water  by  H20, 
thus  indicating  that  this  molecule  consists  of  two 
atoms  of  hydrogen  and  one  atom  of  oxygen,  as  just 
stated ;  also  indicating,  further,  that  the  weight  of 
this  molecule  is  16  -f-  2  =  18 ;  and  still  further  show- 
ing that  in  water  oxygen  and  hydrogen  are  united  in 
the  proportions  by  weight  of  16:  2. 

In  like  manner  we  represent  a  molecule  of  carbonic 
acid  gas  by  C0.2,  a  symbol  which  indicates,  first,  that 
the  molecule  of  carbonic  acid  gas  consists  of  one 
atom  of  carbon  and  two  atoms  of  oxygen  ;  secondly, 
that  the  weight  of  the  molecule  is  12  -f-  2  X  16  =44; 
thirdly,  that  in  carbonic  acid  gas  carbon  and  oxy- 
gen  are   combined    in    the    proportion    of    12  :  32. 


CHEMICAL   REACTIONS.  107 


We  call  these  groups  the   symbols  of  the   different 
substances. 

Every  chemical  process  may  be  regarded  as  the 
breaking  up  of  the  molecules  of  one  or  more  sub- 
stances into  atoms,  and  the  regrouping  of  these  same 
atoms  to  form  the  molecules  of  new  substances.  In 
chemistry  we  technically  call  such  processes  reac- 
tions; the  substances  which  concur  in  the  process 
we  call  the  factors,  and  the  substances  formed  by  the 
process  we  call  the  products  of  the  reaction.  As  no 
atom  can  be  destroyed,  every  atom  coming  from  the 
factors,  and  none  others,  must  be  found  among  the 
products;  and  hence  the  total  weight  of  the  products 
must  be  exactly  equal  to  the  total  weights  of  the 
factors.  Therefore  we  can  represent  such  processes 
by  equations,  writing  on  the  left-hand  side  of  the 
equation  mark  the  symbols  of  the  several  factors 
connected  by  the  sign  of  addition,  and  on  the  right- 
hand  side  the  symbols  of  the  products  in  a  similar 
way.  A  few  illustrations  will  make  clear  the  meaning 
of  such  expressions. 

Grape  Sugar.  Alcohol.  Carbonic  Acid  Gas. 

C6H1206        =        2C2H60        +        2C02 

This  reaction  expresses  the  well-known  fact  that  in 
fermentation  grape  sugar  breaks  up  into  alcohol  and 
carbonic  acid  gas.  The  one  factor  is  the  symbol  of 
a  molecule  of  grape  sugar.  This  single  molecule 
yields  two  molecules  of  alcohol  and  two  molecules  of 
carbonic  acid  gas,  or  four  molecules  in  all.  Notice 
how  we  write  two  molecules  of  alcohol,  using  figures 
to  express  several  molecules,  like  coefficients  in  alge- 


108  CHEMICAL   REACTIONS. 

bra;  and  notice  also  that  there  are  as  many  atoms  of 
each  elementary  substance  in  the  one  molecule  of  the 
single  factor  grape  sugar,  as  in  the  two  molecules  of 
alcohol  and  the  two  molecules  of  carbonic  acid  result- 
ing from  the  decomposition. 

Nitrate  of  Ammonia.  Nitrous  Oxide.  Water. 

N2H408  =  N20  +  2H,0 

(2Xi4)+4+(3Xi6)  =  8o      (2Xi4)+i6  =  44      2(2+16)  =36 

The  second  reaction  expresses  that  the  salt  nitrate 
of  ammonia  yields,  when  heated,  nitrous  oxide  gas 
and  water.  Here,  as  before,  the  atoms  of  the  one 
molecule  which  is  the  factor  of  the  reaction  break 
apart,  and  rearrange  themselves  to  form  one  molecule 
of  nitrous  oxide  gas  and  two  molecules  of  water. 
Since  the  symbols  stand  for  definite  relative  weights, 
the  reaction  informs  us  further  that  from  eighty  parts 
of  the  salt  we  obtain  forty-four  parts  of  nitrous  oxide 
gas  and  thirty-six  parts  of  water. 

Dilute  Sulphuric  Acid.  Zinc.  Zinc  Sulphate.         Hydrogen  Gas. 

(H2S04  +  Aq.)      +     Zn     =     (ZnS04  +  Aq.)     +     H2 

The  third  reaction  represents  the  process  by  which 
hydrogen  gas  is  made  from  dilute  sulphuric  acid  and 
zinc.  It  gives  in  general,  in  regard  to  this  chemical 
change,  information  similar  to  that  we  have  learned 
from  the  two  preceding  examples.  Moreover,  it 
shows  that  the  change  consists  essentially  in  this : 
that  the  atom  of  zinc  replaces  the  two  atoms  of 
hydrogen  in  the  acid ;  when  these  hydrogen  atoms 
pair  together  to  form  molecules  of  hydrogen  gas. 
It  will  be  unnecessary  for  my  present  purpose  to 


VALUE   OF   CHEMICAL   SYMBOLS.  IO9 

dwell  on  other  and  more  abstruse  points  of  significa- 
tion which  this  symbolical  language  conveys.  It  is 
sufficient  if  I  have  made  clear  the  more  obvious 
meaning  and  prepared  the  way  for  a  further  inference, 
which  can  easily  be  drawn  from  the  principles  of  the 
system  which  have  been  thus  far  explained. 

It  can  now  easily  be  seen  that  this  symbolical 
notation  gives  an  admirable  basis  for  classifying 
chemical  compounds;  and  further  that  it  brings  out 
analogies  and  enables  us  to  draw  inferences  which 
otherwise  would  never  have  been  suggested.  If  one 
substance  undergoes  certain  changes  it  is  probable 
that  an  allied  substance,  having  a  similar  constitution 
and  therefore  represented  by  a  like  symbol,  would 
partake  of  similar  changes ;  and  the  analogy  sug- 
gested by  the  symbols  often  leads  us  to  test  our  in- 
ferences by  experiment,  and  thus  we  are  constantly 
led  to  the  discovery  of  new  truths. 

There  is,  however,  a  most  important  difference 
between  a  chemical  reaction  and  a  mathematical 
equation,  which  should  be  always  kept  in  mind. 
From  a  mathematical  equation  any  result  that  can 
be  deduced  by  the  principles  of  algebra  must  in  some 
sense  be  true.  But  in  chemistry  we  have  discovered 
no  such  far-reaching  principles;  and  our  chemical 
reactions  merely  express  the  known  facts  in  regard 
to  each  process  they  represent ;  and  we  can  draw  no 
certain  conclusions  one  step  removed  from  the  facts 
which  the  symbols  signify.  The  notation  is  fruitful 
in  suggestions,  nothing  more. 

When  the  laws  which  govern  the  grouping  of 
chemical  atoms  have  been  formulated  we  may  hope 


IIO  THE   SYLLOGISM. 


for  an  all-embracing  calculus  of  chemical  operations ; 
but  from  want  of  precise  and  exhaustive  knowledge 
of  these  principles,  all  attempts  in  this  direction  have 
been  thus  far  failures.  Nevertheless,  the  conven- 
tional symbolism  of  chemistry  has  been  of  the  very 
greatest  value  in  suggesting  possible  relations  and 
pointing  out  fruitful  lines  of  investigation. 

Of  most  subjects  the  fundamental  conceptions  and 
processes  do  not  admit  of  more  precise  designations 
than  ordinary  language  affords,  and  the  arguments 
which  arise  are  discussed  under  the  conditions  which 
the  science  of  logic  seeks  to  analyze  and  classify  in 
the  various  forms  of  the  syllogism.  We  may  often 
thus  arrive  at  as  complete  certainty  as  by  mathemat- 
ics, —  although  it  is  important  not  to  wander  far  from 
the  boundaries  of  known  truth,  and  to  verify  every 
step  of  our  progress  by  an  appeal  to  observation  or 
experiment.  But  whether  the  conclusions  be  reached 
by  mathematical,  chemical,  or  syllogistic  reasoning, 
the  method  is  essentially  deductive;  and  implicitly 
the  results  were  involved  in  the  premises  with  which 
we  started. 

No  fountain  can  rise  higher  than  its  source,  and 
no  process  of  reasoning,  however  conducted,  can 
mount  above  the  general  principles  or  fundamental 
truths  on  which  the  reasoning  rests.  These  are  the 
essential  conditions  or  premises  of  the  mental  pro- 
cess, and  necessarily  imply  previous  generalizations 
which  were  acquired  by  induction.  While,  however, 
we  admit  that  the  results  of  deductive  reasoning, 
however  conducted,  were  implicitly  contained  in  the 
data  of  the  calculation  or  the  premises  of  the  argu- 


DEDUCTIONS   MUST   BE  TESTED.  Ill 


ment,  we  must  not  infer  that  knowledge  cannot  be 
increased  by  such  means. 

Before  an  Infinite  Intelligence  all  the  relations  of 
truth  must  be  open ;   but  how  far  this  is  from  being 
possible  to  a  finite  intelligence  we  have  all  sadly  ex- 
perienced;   and  to  man  the  deductions  of  science  are 
as  much  new  truths  as  if  they  were  direct  revelations  ; 
and    the    greatest   discoveries   have    been    made   by 
strictly  deductive  processes  of  investigation.     Indeed, 
as  I  have  already  said,  knowledge  is  enlarged  chiefly 
by  deductive  reasoning,  verified  by  observation  and 
experiment.     Nevertheless,  as  has  also  been  said,  de- 
duction implies  previous  induction,  and  differs  from 
induction,  not  in  that  its  results  are  less  real  or  less 
novel   to   men,   but  in   that  they  are  of  a  different 
order,  and  sustain  different  relations.     What  this  dif- 
ference is,  we  shall  still  further  endeavor  to  illustrate. 
If  a  general  principle,  like  the  law  of  gravitation, 
is   absolutely  true,  everything  that  can  be  deduced 
from  it  by  legitimate  processes  must  be  equally  true. 
But  in  science  we  have  constantly  to  deal  with  induc- 
tions  which    are    only   partial    truths.     Under   such 
circumstances,   entire  reliance  cannot  be  placed  on 
the  deductions ;    and  hence  the  importance  of  testing 
each  step  of  the  argument  by  observation  or  experi- 
ment.    In  proportion  as  the  predictions  are  verified, 
the  greater  confidence  do  we  place  in  the  universality 
of  the  principle  on  which  the  deductions  were  based. 

Excepting,  however,  the  axioms  of  mathematics, 
the  laws  of  motion,  and  a  few  similar  principles,  there 
are  no  generalizations  which  can  be  regarded  as  ab- 
solutely beyond  question ;    and  it  is  conceivable  that 


112  CAUSES   OF   UNCERTAINTY. 

conditions  may  arise  under  which  even  the  law  of 
gravitation  will  fail.  It  is,  therefore,  only  in  pure 
mathematics  and  in  simple  physical  problems,  that 
we  can  feel  safe  in  our  deductions  without  submitting 
them  to  the  test  of  experience. 

Uncertainty  in  regard  to  the  results  of  deduction 
may  arise,  not  only  from  failure  in  the  particular  case 
of  the  general  principle  on  which  dependence  has 
been  placed,  but  also  from  inherent  difficulties  in  the 
deductive  process.  In  algebra,  mathematicians  have 
not  been  able,  except  in  special  cases,  to  obtain  com- 
plete solutions  of  equations  of  higher  degrees  than 
the  fourth,  and  the  ingenious  methods  which  they 
employ  with  problems  which  give  equations  of  a 
higher  order,  yield  at  best  only  partial  solutions.  So 
also  in  chemistry,  the  methods  of  analysis  give  only 
approximate  results,  and  for  this  reason  the  conclu- 
sions based  upon  them  are  more  or  less  indefinite. 
Hence  arises  the  importance,  in  all  physical  science, 
of  the  discussion  of  what  is  called  the  probable  error 
of  observations,  and  also  of  the  personal  error  of  the 
observer ;  and  in  this  connection  a  few  words  on  the 
errors  which  are  inherent  in  all  scientific  methods, 
and  necessarily  affect  their  results,  will  not  be  out  of 
place. 

Even  among  scholars,  who  while  familiar  with  the 
general  results  of  science  are  strangers  to  its  methods, 
there  is  a  common  misapprehension  in  regard  to  the 
certainty  of  scientific  conclusions,  or  in  regard  to  the. 
infallibility  of  scientific  evidence.  Physical  science 
is  constantly  spoken  of  as  exact,  and  as  yielding  pos- 
itive proofs,  in  contrast  with  the  moral  sciences,  whose 


MEASUREMENTS   NEVER   ABSOLUTELY  EXACT.       113 

results  are  less  definite  and  more  questionable.  As 
regards  physical  science  all  this  is  to  a  great  extent 
true,  — since  a  large  mass  of  the  facts  which  have  been 
established  in  relation  to  the  phenomena  of  nature 
are  as  certain  as  the  axioms  of  geometry ;  but  no  re- 
sults of  measurements  are  absolutely  exact,  and  the 
accredited  values  have  every  possible  degree  of  pre- 
cision. There  are  very  few  magnitudes  of  nature 
which  are  known  accurately  within  a  thousandth  part 
of  their  value;  and  our  knowledge  of  such  funda- 
mental quantities  is  often  in  error  to  the  extent  of 
one-tenth.  To  scientific  experts  this  is  a  familiar 
fact,  and  in  all  their  deductions  they  take  into  ac- 
count the  resulting  uncertainty;  but  literary  men  are 
apt  to  reason  as  if  they  thought  everything  accepted 
in  science  was  known  with  equal  exactness,  and  are 
led  into  error  by  this  unconscious  assumption.  A 
very  small  experience  with  the  reality  would  dispel 
this  illusion ;  and  hence  the  importance  to  all  scholars 
of  that  limited  experience  with  scientific  methods 
which  will  give  an  understanding,  not  only  of  the  true 
relations  of  scientific  facts,  but  also  of  the  limitations 
of  scientific  results. 

The  unavoidable  errors  of  scientific  methods  may 
be  classed  under  two  heads;  and  we  must  distin- 
guish the  constant  errors,  which  are  inherent  in  the 
process  employed  or  in  the  observer  himself,  from 
the  accidental  errors,  which  are  determined  solely  by 
chance.  The  last  are  as  likely  to  be  in  one  direction 
as  another;  while  the  first,  under  the  same  conditions, 
are  always  in  the  same  direction. 

Of  the  two  classes  of  errors  the  accidental  errors 


114  ACCIDENTAL   ERRORS. 

are  by  far  the  less  important,  and  to  a  great  extent 
can  be  eliminated  by  multiplying  observations.  The 
arithmetical  mean  of  several  observations  is  always 
far  more  trustworthy  than  any  single  observation, 
and  the  theory  of  probabilities  gives  us  in  such 
cases  a  method  of  estimating,  not  only  the  probable 
error  of  any  one  observation  of  the  set,  but  also  the 
probable  error  of  the  mathematical  mean.  The  dis- 
cussion of  probable  errors  is  one  of  the  most  impor- 
tant applications  of  mathematics,  which  is  generally 
known  as  the  "  Method  of  Least  Squares;"  and  it  is 
certainly  a  most  remarkable  result  of  science  that  what 
would  seem  to  be  at  first  sight  so  wholly  accidental 
and  utterly  lawless,  should  be  found  to  be  regulated 
by  definite  principles  and  become  a  matter  of  exact 
computation.  Yet  this  is  strictly  true.  If,  for  ex- 
ample, we  first  eliminate  from  a  series  of  observa- 
tions of  some  definite  quantity,  as  for  example  the 
value  of  an  angle,  all  evident  mistakes  and  known 
causes  of  error,  there  will  still  remain  differences  in 
the  results,  which  will  appear  the  more  pronounced 
in  proportion  as  we  seek  to  secure  greater  accuracy 
in  our  measurements.  Such  differences  we  call  acci- 
dental errors,  and  they  are  due  to  numberless  causes 
which  we  cannot  estimate,  depending  upon  the  im- 
perfection of  our  instruments,  or  of  our  senses,  or  on 
the  varying  conditions  under  which  all  experiments 
must  be  made.  Now  if  we  take  the  arithmetical 
mean  of  all  the  numbers  obtained  as  the  most  prob- 
able value,  and  call  the  difference  between  the  mean 
value  and  each  separate  value  the  error  of  that 
observation,  it  will  always  appear, — 


"  PROBABLE   ERROR."  115 

First,  that  small  errors  are  more  frequent  than 
large  ones. 

Secondly,  that  positive  and  negative  errors  are 
equally  frequent. 

Thirdly,  that  very  large  errors  do  not  occur. 


Observations. 

V. 

v\ 

0        /      // 

Il6   43   44.45 

5.19 

26.94 

SO-55 

— 0.91 

0.83 

50.95 

— 1.31 

1.72 

48.90 

0.74 

0.55 

49-20 

0.44 

0.19 

48.85 

0.79 

0.63 

47.40 

2.24 

5.02 

47-75 

1.89 

3-57 

51.05 

— 1.41 

2.00 

47.85 

1.79 

3.20 

50.60 

— 0.96 

0.92 

48.45 

1. 19 

1.42 

51-75 

— 2. 1  I 

4-45 

49.00 

O.64 

0.41 

52-35 

— 2.71 

7-34 

51.05 

—  1. 41 

2.00 

51.70 

— 2.06 

4.24 

49.05 

O.59 

o-35 

50-55 

— O.9I 

0.83 

49.25 

o-39 

0.15 

46.75 

2.89 

8-35 

49.25 

o-39 

0.15 

53-4o 

—3-76 

14.14 

5i-3o 

—1.66 

2.75 

s=  1 1 6°  43'  49".64 

71  =  24 

2  v-  =  92.15 

v  =  0.6745  l/S  = 

i-"35 

r-3S          „ 

V24 

On  these  fundamental  principles  derived  from  ex- 
perience all  our  reasoning  on  the  subject  is  based. 


Il6  CONSTANT   ERROR. 


An  examination  of  tables  of  observations,  such  as  are 
given  in  the  Reports  of  our  Coast  Survey,  may  be 
very  instructive  as  they  exhibit  in  a  most  remarkable 
manner  the  principles  we  have  been  endeavoring  to 
illustrate. 

Thus,  in  a  series  of  twenty-four  measurements  of 
an  angle  of  the  primary  triangulation  made  at  the 
station  Pocasset  in  Massachusetts,  and  cited  on  the 
previous  page,  all  the  above  principles  are  strikingly 
illustrated ;  and  it  further  appears  that  while  the 
largest  difference  from  the  mean  value  amounts  to 
5".  19,  the  probable  error  of  a  single  observation  is 
but  i"-3  5,  and  the  probable  error  of  the  mean  value 
only  o".28.  The  term  "  probable  error,"  as  thus  used, 
has  a  conventional  meaning,  and  simply  signifies 
that  there  is  an  even  chance  that  the  true  value  is 
within  the  limit  assigned. 

But  while  such  accidental  errors  as  have  been  de- 
scribed are  constantly  reminding  us  of  the  restric- 
tions of  our  powers,  they  are  limited  in  extent,  and 
as  also  we  have  seen,  can  be  to  a  large  extent  elim- 
inated. Not  so  with  the  constant  errors  which  arise 
from  unknown  causes  of  various  kinds,  or  even  from 
the  idiosyncrasies  of  the  observers.  These  may  be 
very  large,  are  likely  to  operate  only  in  one  direc- 
tion, and  may  thus  seriously  vitiate  our  results. 
They  are  an  insidious  foe  against  which  all  our 
watchfulness  and  care  cannot  protect  us,  an  enemy 
in  the  dark,  of  whose  direction  and  magnitude  we 
can  form  no  estimate.  These  constant  errors  are 
the  chief  source  of  difficulty  in  all  experimental 
investigation  ;   they  have  occasioned  incalculable  loss 


CONSTANT   ERROR.  117 

of  labor;  and  besides  discouraging  the  investigator, 
they  frequently  introduce  an  element  of  uncertainty 
into  his  results.  Years  of  conscientious  and  careful 
investigation  have  thus  been  rendered  unavailing  by 
an  unsuspected  error  which  has  vitiated  the  whole 
work  ;  and  values  which  had  been  regarded  as  among 
the  best-established  data  of  science  have  subsequently 
been  found  to  be  erroneous,  owing  to  the  discovery  of 
a  source  of  error  in  the  method  by  which  they  were 
determined.  A  remarkable  example  from  my  own 
experience  will  illustrate  these  important  points. 

The  atomic  weights  are  among  the  most  important 
constants  of  science,  and.  the  accurate  determination 
of  these  numerical  values  involves  analytical  work  of 
great  refinement  and  accuracy.  In  1856  Schneider, 
of  Berlin,  made  a  determination  of  the  atomic  weight 
of  antimony,  and  obtained  the  number  120.3.  The 
work  was  done  with  all  the  skill  and  precision  that  a 
master  of  analytical  chemistry  could  devise,  and  every 
known  and  conceivable  cause  of  error  appeared  to 
have  been  foreseen  and  allowed  for.  Eight  separate 
determinations  were  made,  no  one  of  which  differed 
from  the  extreme  value  more  than  0.23.  Neverthe- 
less, a  year  later  Mr.  W.  P.  Dexter,  working  with  a 
different  method,  but  with  equal  refinement,  obtained 
as  a  mean  of  ten  determinations  122.34,  that  is,  a  value 
two  whole  units  greater  than  the  first,  —  although  here 
again  the  results  of  the  several  determinations  agreed 
so  closely  with  each  other  that  the  maximum  differ- 
ence from  the  mean  value  was  only  0.14.  At  very 
nearly  the  same  time  the  famous  chemist  Dumas 
made  at  Paris  still  a  third  independent  determination 


Il8  CONSTANT   ERROR. 

of  the  constant  under  consideration,  using  a  wholly 
different  method  from  either  Schneider  or  Dexter, 
and  obtained  122.00,  —  nearly  the  same  value  as  Dex- 
ter, and  with  a  similar  close  agreement  between  the 
results  of  four  separate  experiments.  The  deserved 
reputation  of  Dumas  for  accuracy,  skill,  and  judgment 
gave  such  authority  to  his  result  that  it  was  at  once 
adopted,  and  remained  for  twenty  years  the  accepted 
value  of  the  atomic  weight  of  antimony. 

In  1877  I  was  myself  led  to  repeat  the  determina- 
tion of  Schneider,  only  reversing  his  processes,  and 
obtained  very  closely  his  value  of  about  120.  This 
led  me  to  repeat  the  process  of  Dumas,  when  I  ob- 
tained a  still  closer  confirmation  of  the  larger  number, 
122.  What  could  be  the  occasion  of  this  large  differ- 
ence? The  discrepancy  could  not  arise  from  the 
ordinary  errors  of  analytical  work,  which  in  either 
process  was  far  less  than  this ;  as  the  close  agreement 
of  the  separate  results  obtained  by  the  same  process 
plainly  showed.  There  must  be  some  unknown  con- 
stant error  affecting  one  or  both  of  the  results.  To 
confirm  this  conclusion  I  made  a  third  determination 
of  the  atomic  weight,  by  a  process  which  had  never 
been  employed  before  and  which  admitted  of  great 
accuracy.  This  gave  me  with  great  exactness  the 
first  value,  120;  and  when  a  fourth  determination 
by  still  another  process  also  gave  the  same  value,  I 
felt  convinced  that  the  higher  number,  which  had 
been  so  long  accepted,  was  the  one  which  had  been 
affected  by  the  constant  error,  but  I  did  not  feel  sat- 
isfied until  I  detected  the  cause  of  the  error  and 
showed  in  what  it  consisted. 


COINCIDENCES   MAY  BE   ILLUSORY.  IIO, 

This  experience  is  a  fair  illustration  of  what  is  con- 
stantly met  with  in  scientific  investigation,  and  indi- 
cates moreover  the  only  general  method  of  ferreting 
out  constant  errors.  When  determinations  of  a  given 
value  made  by  essentially  different  methods  are  ac- 
cordant, we  have  a  well-grounded  confidence  in  their 
accuracy;  but  mere  coincidences  of  numbers  obtained 
in  the  same  way  are  no  proof  of  truthfulness,  for  con- 
stancy of  results  often  arises  from  constancy  of  errors. 
I  would  that  I  could  convey  to  you  the  full  force  of 
the  impression  which  is  left  on  the  mind  after  repeated 
experiences  such  as  I  have  described.  The  helpless- 
ness which  one  feels  while  thus  working  in  the  dark 
gives  a  reality  to  the  sense  of  the  limitations  of  our 
knowledge,  of  which  so  much  is  said  and  so  little 
appreciated.  If  anything  will  lead  man  to  hold  his 
knowledge  in  humility  and  reverence  it  is  the  con- 
sciousness that  results  so  laboriously  obtained  may 
be  invalidated  by  circumstances  over  which  he  has 
no  control,  and  of  whose  existence  he  is  wholly 
unaware. 

I  would  that  I  could  also  give  an  adequate  concep- 
tion of  the  great  amount  of  conscientious  work  which 
is  expended  on  the  deductions  of  science  for  the  sole 
love  of  truth.  Were  it  possible,  I  am  sure  that  your 
respect  for  the  scientific  investigator  would  be  greatly 
increased  and  your  belief  in  his  sincerity  established, 
however  mistaken  you  may  at  times  deem  his  opin- 
ions or  his  judgment.  Of  course  in  the  cultivation 
of  science,  as  in  every  other  pursuit  of  life  there  is 
abundant  room  for  the  display  of  unworthy  motives 
and  ignoble  passions ;  but  I  venture  to  assert  that 
9 


120        COMPLEXITY   OF  NATURAL   PHENOMENA. 

there  is  no  class  of  men  in  the  world  among  whom  is 
found  more  unselfish  devotion  and  more  personal  sac- 
rifice than  among  the  great  army  of  scientific  workers. 
The  love  of  abstract  truth  may  be  a  much  lower 
motive  than  the  love  of  man,  but  it  equally  calls 
forth  the  very  noblest  qualities  of  the  mind.  More- 
over, in  most  cases  the  constancy  and  courage  of  the 
scientific  investigator  meet  with  no  reward  except 
the  satisfaction  which  unselfish  duty  conscientiously 
discharged  always  brings;  and,  as  Professor  Tyndall 
has  said,  "  There  is  a  morality  brought  to  bear  on 
such  matters  which  in  point  of  severity  is  probably 
without  a  parallel  in  any  other  domain  of  intellectual 
action." 

The  difficulties  of  scientific  deduction  are  further 
vastly  increased  by  the  circumstance  that  in  the 
phenomena  of  nature  the  effects  of  various  causes  are 
usually  so  correlated  and  intertwined  that  the  task  of 
separating  them  or  of  determining  their  precise  rela- 
tions is  well-nigh  hopeless.  Take  such  an  apparently 
simple  phenomenon  as  the  rise  of  the  column  of  mer- 
cury in  the  stem  of  such  a  thermometer  as  is  univer- 
sally used  to  measure  changes  of  temperature.  The 
height  of  the  mercury  column  depends  on  a  number 
of  causes  which  combine  to  produce  the  result  we 
observe.  Besides  slight  effects  arising  from  mechani- 
cal strain  or  irregularities  of  the  tube,  we  must  distin- 
guish, first,  the  expansion  of  the  mercury,  of  which 
the  rate  slowly  increases  as  the  temperature  rises, 
and  which  tends  to  raise  the  column ;  secondly,  the 
expansion  of  the  glass,  which  is  very  irregular  and 
tends  to  depress  the  column ;  thirdly,  certain  obscure 


ILLUSTRATED   BY  THE   THERMOMETER.         121 

changes  in  the  texture  of  the  glass  itself  which  act 
slowly,  but  which  on  the  whole  tend  slightly  to  raise 
the  column.  It  is  true  that  the  last  two  effects  are  so 
inconsiderable  as  compared  with  the  first  that  they  do 
not  seriously  interfere  with  the  use  of  the  instrument 
as  a  rough  measure  of  temperature  in  our  houses. 
But  when  in  scientific  investigation  we  seek  an  exact 
measure,  to  the  hundredth  of  a  centigrade  degree, 
they  interfere  most  seriously ;  so  that  while  small  dif- 
ferences of  temperature  may  be  thus  closely  estimated 
under  restricted  conditions,  we  have  no  means  of  meas- 
uring large  changes  of  temperature  with  any  such 
approach  to  exactness ;  and  beyond  a  certain  limit 
of  accuracy  the  use  of  this  simple  instrument  is  one 
of  the  difficult  problems  of  science.  Even  in  the 
ordinary  use  of  the  thermometer  for  determining  the 
temperature  of  the  external  air,  very  considerable 
differences  may  be  caused  by  radiation,  from  the 
ground,  from  the  sky,  or  from  surrounding  objects, 
depending  on  the  exposure  of  the  instrument;  and 
the  discrepancies  between  neighbors  on  the  state  of 
the  weather  —  which  are  often  so  amusingly  paraded 
—  are  simple  illustrations  of  what  is  very  familiar  to 
every  scientific  observer. 

If,  now,  instead  of  using  the  thermometer  as  a 
measure  of  temperature,  we  seek  to  estimate  each  of 
the  separate  effects  whose  combined  action  the  in- 
strument registers,  we  are  met  at  once  with  almost 
insuperable  difficulties,  and  the  approximate  solution 
of  this  problem  by  Regnault  was  one  of  the  triumphs 
of  experimental  science.  By  an  ingenious  method  of 
experimenting,  first  devised  by  Dulong  and  Petit,  he 


122  ILLUSTRATED   BY  THE   BAROMETER. 

succeeded  in  measuring  the  absolute  expansion  of 
mercury,  and  when  this  was  known  he  could  estimate 
the  expansion  of  the  bulb  and  tube  of  which  the 
thermometer  was  made. 

As  with  the  thermometer,  so  again  with  the  barom- 
eter. The  height  of  the  mercury  column  in  the 
barometer  depends  not  only  on  the  pressure  of  the 
air  which  the  instrument  is  intended  to  measure,  but 
is  also  perceptibly  influenced  by  a  variety  of  other 
causes,  such  as  temperature,  the  force  of  gravity,  and 
capillary  attraction.  For  some  of  these  effects  we 
can  make  accurate  corrections,  but  for  others  we  can- 
not ;  so  that  the  readings  of  a  barometer  made  with 
the  greatest  refinement  at  Paris,  are  not  strictly  com- 
parable with  those  of  one  made  with  equal  care  at 
New  York;  and  the  only  way  in  which  we  could 
make  an  exact  comparison  would  be  by  transport- 
ing the  same  instrument  to  and  fro  between  the  two 
places,  as  we  might  a  metre  measure. 

These  are  but  two  examples  of  a  universal  experi- 
ence. All  the  phenomena  which  we  attempt  to 
observe  are  obscured  by  other  phenomena  with  which 
they  are  associated,  and  all  the  instruments  with 
which  we  make  our  measurements  are  more  or  less 
fallible  and  faulty.  Hence  the  general  principles  we 
deduce  from  our  observations  partake  of  the  same 
limitations.  This  is  no  hair-splitting  metaphysical 
refinement ;  for,  with  the  exception  of  a  few  of  the 
great  primary  principles  of  nature,  like  the  law  of 
gravitation  or  the  conservation  of  energy,  there  is 
hardly  one  of  the  so-called  laws  of  physics  or  chem- 
istry which   we    should    implicitly  trust    in    circum- 


LIMITATIONS   OF   HUMAN   FACULTIES.  1 23 

stances  widely  differing  from  those  under  which  they 
are  established.  As  a  rule,  mathematical  deductions 
are  based  not  on  actual  qualities  of  bodies,  but  on 
ideal  relations  which  have  no  exact  material  repre- 
sentatives. There  are  no  such  things  as  the  rigid 
bars,  the  simple  pendulums,  and  perfect  fluids  of  our 
theoretical  mechanics.  These  are  as  much  abstrac- 
tions as  are  points,  lines,  and  surfaces ;  and  in  many 
respects  the  sciences  of  mechanics  and  astronomy  are 
as  much  products  of  pure  thought  as  geometry. 

In  order  to  bring  the  problems  suggested  by  nature 
within  the  grasp  of  his  analysis,  the  mathematician  is 
forced  to  simplify  them  by  leaving  out  of  considera- 
tion every  accessory  circumstance.  As  the  late  Stan- 
ley Jevons  has  so  strikingly  said  in  his  "  Principles 
of  Science,"  "  The  faculties  of  the  human  mind,  even 
when  aided  by  the  wonderful  powers  of  abbreviation 
conferred  by  analytical  methods,  are  utterly  unable 
to  cope  with  the  complications  of  any  one  real  prob- 
lem." Of  course  the  mathematician  endeavors  to 
approach  the  natural  problem  as  nearly  as  possible, 
and  in  most  cases  the  differences  do  not  alter  essen- 
tially the  character  of  the  solution  within  reasonable 
limits ;  but  they  do  narrow,  and  often  most  seriously, 
the  scope  of  the  deductions. 

Many  educated  men  who  are  familiar  with  the 
great  definiteness  of  the  elementary  mathematics, 
form  an  exaggerated  conception  of  the  power  and 
infallibility  of  mathematical  analysis ;  and  from  their 
limited  observation  infer  that  mathematics  has  the 
power  of  solving,  in  a  perfect  manner,  all  problems 
which  involve  only  quantitative  relations.     And  when 


124      LIMITATIONS   OF   MATHEMATICAL  ANALYSIS. 

we  consider  what  they  have  accomplished,  the  powers 
of  such  minds  as  those  of  Lagrange  and  Laplace  do 
appear  almost  miraculous.  But  when  we  compare 
the  simple  problems  which  they  have  solved  with 
the  complicated  relations  which  modern  investigation 
has  revealed,  even  the  powers  of  such  masters  are 
seen  to  be  inadequate ;  and  to  follow  out  the  deduc- 
tions from  principles  already  known,  appears  to  be  a 
hopeless  undertaking. 

Jevons,  whom  we  have  just  quoted,  also  says 
that  "  if  a  mathematical  problem  were  selected  by 
pure  chance  out  of  the  whole  variety  which  might  be 
proposed,  the  probability  is  infinitely  slight  that  a 
human  mathematician  could  solve  it."  Let  me  cite 
a  familiar  instance. 

The  undulatory  theory  of  light  presents  relations 
peculiarly  favorable  to  mathematical  analysis,  and 
from  which  a  great  wealth  of  deductions  has  been 
drawn.  But  the  colors  of  the  rainbow,  or  more  gen- 
erally the  whole  range  of  phenomena  attending  the 
dispersion  of  light  by  refracting  media,  still  remain 
essentially  unexplained  ;  and  the  most  that  Cauchy  — 
perhaps  the  ablest  mathematician  of  this  century  — 
was  able  to  accomplish  was  to  show  that  under 
certain  assumed  circumstances  such  a  result  might 
follow  from  the  undulatory  theory,  and  to  make  evi- 
dent that  the  complete  solution  of  the  problem  was 
beyond  our  present  powers  of  mathematical  analysis. 

So  also  in  regard  to  the  finality  of  mathematical 
deductions.  It  is  a  common  remark  that  figures 
cannot  lie ;  but,  as  many  have  found  to  their  cost, 
they  may  be    made   to    bewilder   the    ignorant  and 


LIMITATIONS   OF   MATHEMATICAL   ANALYSIS.      1 25 


cover  up  a  great  deal  of  error.  Mathematical  results 
are  conclusive  only  as  regards  the  assumed  relations 
with  which  the  analysis  starts ;  and  these  may  be  so 
different  from  the  relations  of  any  real  problem  of 
nature  as  to  render  the  conclusions  inapplicable  in 
any  specific  case. 

It  should  be  clearly  understood  that  there  is  noth- 
ing mysterious  about  mathematics ;  that  even  when 
its  processes  cannot  be  followed  except  by  adepts, 
its  premises  and  conclusions  can  always  be  clearly 
stated.  The  operations  or  processes  of  thought 
which  it  combines  by  means  of  its  admirable  sym- 
bolism, are  severally  perfectly  intelligible  ;  but  in  the 
multiplicity  of  the  possible  relations  confusion  may 
readily  arise,  and  it  requires  a  keen  intellect,  with 
great  power  of  abstraction  and  concentration,  to  trace 
out  these  relations  to  their  consequences.  Without 
the  symbols  the  task  would  have  been  beyond  the 
best  human  faculties,  except  in  the  simplest  prob- 
lems ;  and  even  with  all  the  aids  which  an  ingenious 
symbolism  can  give,  the  power  of  combination  is 
very  limited  and  wholly  inadequate  to  grasp  the 
complex  relations  which  the  real  phenomena  of 
nature  invariably  present. 

In  thus  dwelling  on  the  limitations  of  scientific 
deductions,  I  am  not  overlooking  its  grand  results. 
These  last  speak  for  themselves,  and  are  fully  appre- 
ciated and  honored.  They  have  become  an  impor- 
tant element  of  our  daily  life,  and  have  profoundly 
modified  the  thought  of  our  time ;  and  while  we  are 
thankful  for  the  acquisitions  of  the  past,  we  look  for 
still  greater  rewards  in  the  near  future.     It  is  well, 


126  RESERVE   OF   SCIENCE. 

however,  at  times,  instead  of  looking  back  at  what 
has  been  done,  to  look  forward  to  what  remains  to 
be  accomplished,  and  to  compare  our  knowledge,  not 
with  what  our  fathers  knew,  but  with  the  universe 
about  us.     Courage,  enterprise,  and   confidence  are 
great  virtues,  but  so  are  also  modesty,  caution,  and 
reservation   of  judgment.      When    men   venture    to 
frame  theories  of  creation  and  claim  that  the  existing 
order   might   have    resulted  from   the    principles    of 
action   now  known,  I   am   at  a  loss  which  most  to 
admire,  their  unconsciousness  or  their  boldness.     My 
only  attempt  at  refutation  would  be   to    ask   these 
would-be  world-builders   to  work   themselves  for   a 
while  in  unravelling  a  web  of  material  conditions  in 
the  darkness  of  the  unknown.     If  they  work  faith- 
fully I  am  sure  that  in  distinguishing  the  ends  of  a 
few  threads  they  will  be  rewarded  for  all  their  pains ; 
but  I  am  equally  confident  that  at  the  same  time 
they  will  gain  the  conviction  that  hidden  causes,  as 
yet  unsuspected,   may  intervene  in  the  commonest 
phenomena  of  nature.     Do  not  think  I  am  a  pessi- 
mist because  I  feel  it  my  duty  to  emphasize  these 
well-known  facts.     In  the  admirable  work  of  Jevons, 
to  which  I  have  referred,  you  will  find  the  same  gen- 
eral doctrine  still  more  emphatically  stated  and  more 
fully  illustrated. 


THE  ATOMIC   THEORY.  \2J 


LECTURE   V. 

EXAMPLES    OF   SCIENTIFIC    INVESTIGATION. 

IN  the  present  lecture  I  shall  ask  your  attention  to 
two  examples  of  scientific  investigation,  which 
will  give  a  better  idea  than  can  any  general  dis- 
cussion, of  the  difficulties  and  uncertainties  which 
perplex  the  student  in  almost  every  attempt  to  sub- 
stantiate the  deductions  from  scientific  generaliza- 
tions. I  select  the  first  example  because  it  is  within 
my  own  very  recent  experience ;  and  although  the 
history  of  science  may  present  far  more  striking 
illustrations,  I  can  speak  of  the  perplexities  incident 
to  this  investigation  from  personal  knowledge ;  and 
as  the  results  of  the  investigation  have  only  recently 
been  published,1  this  fresh  example  may  have  the 
interest  of  novelty. 

The  atomic  theory  is  as  old  as  Greek  philosophy, 
and  the  best  and  most  original  exposition  of  the 
theory  is  still  to  be  found  in  the  famous  heroic  poem 
of  Lucretius,  "  De  Rerum  Natura,"  which  appears  to 
have  been  written  about  58  B.  c.  The  adaptation  of 
the  theory  to  explain  the  definite  combining  propor- 
tions of  chemistry  was   made   by  John   Dalton,   of 

1  Published  in  Proceedings  of  the  American  Academy  of 
Arts  and  Sciences,  vol.  xxiii.  p.  119. 


128  prout's  hypothesis. 

Manchester,  in  the  early  part  of  the  present  century, 
and  since  then  these  combining  proportions  have 
generally  been  called  atomic  weights. 

It  was  obvious  from  the  first  that  of  all  the  ele- 
mentary substances  hydrogen  gas  must  have  the 
smallest  atomic  weight,  and  it  was  a  natural  inference 
that  the  atoms  of  all  the  elementary  substances 
might  be  aggregates  of  this  smallest  indivisible  unit. 

Such  a  theory  was  in  harmony  with  the  philosoph- 
ical conception  that  in  the  last  analysis  all  materials 
could  be  reduced  to  the  same  ultimate  essence,  and 
that  differences  of  qualities  depended  on  the  differ- 
ent affections  of  which  this  primordial  material  was 
susceptible.  This  theory  was  strongly  advocated  by 
Dr.  Prout,  an  eminent  physician  in  London,  during 
the  first  half  of  this  century,  and  the  author  of  one 
of  the  well-known  Bridgewater  Treatises ;  and  is 
known  in  science  as  "  Prout's  hypothesis."  Obvi- 
ously, if  this  theory  be  true  it  would  follow  that  all 
the  atomic  weights  must  be  multiples  of  the  atomic 
weight  of  hydrogen ;  and  if  this  last,  as  is  usual,  be 
taken  as  the  unit  of  the  system,  the  values  of  all 
other  atomic  weights  must  be  expressed  in  whole 
numbers.  Here,  then,  was  an  obvious  deduction, 
which,  if  not  substantiated  by  experiment  must  be 
fatal  to  Prout's  hypothesis,  an  induction  on  trial. 

At  the  time  when  Prout  wrote,  the  accepted  values 
of  many  of  the  smaller  weights  were  in  accordance 
with  his  views ;  and  the  methods  of  chemical  anal- 
ysis, by  which  the  combining  proportions  of  the 
elementary  substances  were  determined,  were  not 
sufficiently  accurate  to  distinguish,  in  the  case  of  the 


DUMAS'S   CONCEPTION.  129 


higher  atomic  weights,  even  the  difference  of  a  whole 
unit.  As  analytical  methods  were  improved,  marked 
discrepancies  with  the  theory  appeared;  but  so 
strong  a  hold  had  the  conception  taken  on  the  minds 
of  chemical  students  that  these  anomalies  were  over- 
looked or  attributed  to  errors  of  observation;  and 
for  many  years  it  was  customary  in  works  on  chem- 
istry, to  give  as  the  values  of  the  atomic  weights  the 
nearest  whole  numbers,  instead  of  the  actual  mean 
of  the  observed  values,  and  the  practice  is  still  con- 
tinued in  many  works  of  accepted  authority. 

At  an  early  period  in  the  discussion,  a  marked 
exception  to  the  theory  had  appeared  in  one  of 
the  smaller  and  best  known  of  the  atomic  weights. 
The  combining  proportion  of  chlorine,  which  forms 
with  metallic  silver  one  of  the  best  defined  chemical 
compounds,  could  be  determined  with  great  accu- 
racy; and  all  the  experiments  gave  a  value  for  its 
atomic  weight  closely  approximating  35.5.  This, 
and  a  few  other  similar  facts,  led  the  late  Professor 
Dumas  of  Paris  to  entertain  the  idea  that  the  atomic 
weights,  if  not  all  multiples  of  the  whole  hydrogen 
atom,  might  be  multiples  of  the  half  or  quarter  atom  ; 
or,  in  other  words,  that  the  hydrogen  atom  might 
itself  be  an  aggregate  of  two  or  more  smaller  masses, 
which  were  the  real  units  of  the  system ;  and  he  was 
thus  led  to  undertake  the  redetermination  of  a  large 
number  of  the  atomic  weights,  with  the  view  of  test- 
ing this  modification  of  the  original  conception.  His 
experiments  were  conducted  with  wonderful  skill; 
and  many  of  the  new  values  he  obtained  for  the 
atomic    weights    are    still    universally   accepted    by 


130  INVESTIGATION   OF   STAS. 

chemists.  But  the  results  had  little  bearing  on  the 
question  at  issue ;  for  it  is  obvious  that  by  taking 
the  unit  small  enough  any  result  could  be  regarded 
as  an  even  multiple  of  this  unit  within  the  limit  of 
experimental  errors. 

Soon  after  the  publication  of  Dumas's  paper,  Profes- 
sor Stas  of  Brussels  undertook  a  work  of  still  greater 
magnitude.  Stas  had  never  been  a  believer  in  the 
hypothesis  of  Prout,  and  his  aim  was  to  push  the 
analytical  work  to  such  a  degree  of  refinement  as  to 
show  conclusively  that  the  results  could  not  possibly 
be  reconciled  with  any  modification  of  that  theory. 

Stas  had  been  an  associate  of  Dumas,  and  the  lat- 
ter always  spoke  of  his  former  assistant  in  terms  of 
the  highest  admiration,  declaring  that  he  was  the  most 
accomplished  experimentalist  he  had  ever  known. 
Thus  Stas  brought  to  the  new  investigation  the 
highest  skill,  and,  moreover,  his  position  as  the  di- 
rector of  the  Belgian  mint  gave  him  command  of 
means  and  appliances  which  enabled  him  to  work 
on  far  larger  quantities  of  material  than  any  previous 
experimenter.  As  the  error  of  an  analytical  process, 
other  things  being  equal,  is  less  in  proportion  to  the 
quantity  of  material  used,  the  advantage  gained  from 
the  large  scale  of  his  experiments  was  very  great. 
But  at  the  same  time  these  large  amounts  of  material 
greatly  increased  the  toil  involved ;  and  the  amount 
of  labor  which  Stas  devoted  to  this  investigation  was 
extremely  great  ;  it  can  be  appreciated  only  by 
those  who  are  familiar  with  such  processes.  In  this 
way  however,  Stas  was  able  to  reduce  the  merely 
accidental  errors  of  the  processes  he  employed  within 


STRIKING   FEATURE.  131 

wonderfully  narrow  limits.  He  obtained  values  for 
several  of  the  most  fundamental  atomic  weights, 
which,  though  approaching  whole  numbers,  still  dif- 
fered from  a  multiple  of  the  hydrogen  unit  by  quan- 
tities far  exceeding  the  probable  error.  At  first 
these  results  were  accepted  as  conclusive,  and  it 
seemed  as  if  the  hypothesis  of  Prout  had  been  for- 
ever consigned  to  the  tomb  of  unverified  theories. 

Still,  however,  even  from  Stas's  work  the  remark- 
able fact  appeared  that  the  atomic  weights  thus  de- 
termined with  so  great  labor  and  skill,  though  not 
exact  multiples,  approached  very  nearly  to  exact 
multiples  of  the  atomic  weight  of  hydrogen.  If  the 
several  values  were  absolutely  independent  and  dis- 
tributed by  chance,  the  probabilities  that  they  would 
all  so  nearly  approach  whole  numbers  was  exceed- 
ingly small,  and  there  was  not  one  chance  in  ten 
thousand  that  such  a  distribution  would  occur  as 
Stas's  results  exhibited ;  so  that  on  the  whole  Stas's 
work  seemed  to  indicate  that  there  might  be  some 
truth  in  the  theory  after  all,  if  not  in  the  exact  form 
that  had  been  supposed. 

This  feature  in  the  distribution  of  the  atomic 
weights  became  still  more  marked  as  accurate  values 
of  the  atomic  weights  of  additional  elements  were 
obtained.  Professor  Mallet,  of  the  University  of  Vir- 
ginia, was  one  of  the  first  to  call  attention  to  the  point 
just  mentioned,  in  his  admirable  paper  on  the  atomic 
weight  of  Aluminum,  which  his  very  accurate  and 
accordant  determinations  had  shown  was  very  closely, 
if  not  exactly,  a  whole  number;  and  Professor  F.  W. 
Clarke,  of  Washington,  in  his  work  entitled  "  A  Re- 


132 


ATOMIC   WEIGHTS. 


calculation  of  the  Atomic  Weights,"  after  summing 
up  the  results  of  a  careful  collation  of  all  the  trust- 
worthy determinations  of  these  constants  of  nature, 
writes :  "  Enough  has  been  said  in  this  brief  re- 
sume to  show  that  none  of  the  seeming  exceptions 
to  Prout's  law  are  inexplicable.  Some  of  them  in- 
deed, carefully  investigated,  support  it  strongly.  In 
short,  admitting  half-multiples  as  legitimate,  it  is 
more  probable  that  the  few  apparent  exceptions  are 
due  to  undetected  constant  errors  than  that  the  great 
number  of  close  agreements  should  be  merely  acci- 
dental. I  began  this  recalculation  of  the  atomic 
weights  with  a  strong  prejudice  against  Prout's  hy- 
pothesis, but  the  facts  as  they  came  before  me  have 
forced  me  to  give  it  a  very  respectful  consideration." 
The  following  table  from  the  writer's  work  on  "  Chem- 
ical Philosophy,"  will  make  clear  the  point  we  are 
discussing:  — 

ATOMIC   WEIGHTS,   MOST   ACCURATELY   DETERMINED. 


Hydrogen 

1.002 

Chlorine 

3546 

Lithium 

7.01 

Potassium 

39- 14 

Carbon 

12.00 

Calcium 

40.00 

Nitrogen 

14.04 

Bromine 

79-94 

Oxygen 

16.00 

Silver 

107.93 

Aluminum 

27.02 

Antimony 

120.00 

Sodium 

23.05 

Iodine 

126.85 

Magnesium 

24.00 

Barium 

137-14 

Phosphorus 

31-05 

Thallium 

204. 1 1 

Sulphur 

32.07 

Lead 

206.91 

This  table  includes  all  the  values  of  atomic  weights 
which  up  to  1882  could  be  regarded  as  known  to 
within  1-1000  of  their  value;  and  with  one  or  two 
notable  exceptions,  there  is  no  instance  in  which  the 


DISTRIBUTION   OF  VALUES.  1 33 

value  differs  from  a  whole  number  by  a  quantity 
greater  than  the  possible  error,  though  not  always 
the  "probable  error"  of  the  processes  employed  in 
their  determination. 

Were  these  numbers  wholly  independent  of  each 
other  and  distributed  by  no  law,  we  should  expect  to 
find  every  possible  intermediate  value;  and  the  fact 
that  they  so  nearly  approach  whole  numbers  cannot 
fail  to  produce  on  the  mind  the  impression  that  there 
is  some  influence  which  tends  to  bring  about  this 
result.  It  may  be  that  the  discrepancies  are  due  to 
such  unknown  constant  errors  as  we  have  already 
described,  and  which,  as  every  experimentalist  knows, 
are  always  greatly  to  be  feared.  Or  it  may  be  that 
there  is  in  nature  a  tendency  to  whole  multiples, 
which  in  many  cases  is  not  fully  reached.  This  last 
view,  to  be  sure,  is  not  compatible  with  our  present 
conceptions  of  the  atomic  theory;  but  nature  is  not 
bound  by  this  theory,  nor  should  be  our  philosophy. 

The  force  of  the  evidence  which  such  a  distribution 
of  values  as  the  above  table  presents  was  brought 
home  to  the  writer  in  his  investigation  on  the  atomic 
weight  of  antimony  referred  to  in  the  previous 
lecture.  After  eliminating  various  causes  of  error, 
he  was  enabled  to  determine  with  great  accuracy 
the  atomic  weights  of  antimony,  silver,  and  bromine, 
in  one  and  the  same  series  of  experiments,  and  it 
appeared  that  this  ratio  was  — 

120.00  :  108.00 :  80.00, 
with  a  probable  error  of  less   than  one  in  the  last 
decimal  place.     Here,  then,  is  a  ratio  of  whole  num- 
bers, within  the  1-100  of  a  single  unit;   and  although 


134  REMARKABLE   RATIO. 

the  result  may  be  no  more  impressive  to  others  than 
many  of  the  facts  exhibited  by  the  table,  yet  to 
the  experimentalist  who  after  long  continued  labor 
reaches  such  a  result  as  this,  the  impression  is  in- 
evitable that  there  must  be  something  more  than 
mere  chance  in  such  coincidences. 

Since  the  ratio  of  the  atomic  weights  of  silver  and 
oxygen  have  been  determined  with  great  accuracy, 
we  can  extend  the  above  proportion  to  a  fourth 
term,  the  atomic  weight  of  oxygen,  which  appears 
also  as  a  whole  number,  with  a  somewhat  larger 
probable  error.  Still  we  have  not  reached  the  unit 
of  the  system,  and  when  we  attempt  to  extend  the 
ratio  to  the  atomic  weight  of  hydrogen,  we  find 
that  the  most  probable  value  from  all  experiments 
hitherto  made  gives  the  ratio,  not  of  16  to  I,  but  of 
16  to  1.0025. 

If  now  we  wished  to  refer  to  the  hydrogen  unit 
the  atomic  weights  of  antimony,  silver,  bromine,  and 
oxygen,  whose  ratios  of  whole  numbers  had  been 
determined  as  above,  it  was  only  necessary  to  divide 
all  the  terms  of  the  above  proportion  by  1.0025,  when 
we  obtain  the  series  of  values  given  below  the  others, 
and  all  semblance  of  conformity  to  the  hypothesis 
of  Prout  disappears,  although  of  course  the  second 
series  of  numbers  bear  the  same  ratios  to  each  other 
as  the  first. 

Antimony.  Silver.  Bromine.  Oxygen.  Hydrogen. 

120.00  10S.00  80.00  16.00  1.0025 

119.70  107.73  79-So  15-96  I. 

The  numbers  in  the  lower  of  the  two  proportions 
appear  as  incommensurable  as  Stas  maintained  that 


QUESTION   SUGGESTED.  1 35 

they  were ;  and  the  same  is  true  of  most  of  the 
atomic  weights  when  given,  as  is  usual  in  recent 
text-books  on  chemistry,  on  the  basis  of  the  same 
hydrogen  unit. 

When,  as  the  result  of  my  investigation  in  the 
atomic  weight  of  antimony,  there  were  presented  to 
me  the  ratios  of  whole  numbers,  as  shown  in  the 
first  of  the  above  proportions,  with  the  single  ex- 
ception of  the  atomic  weight  of  hydrogen,  the 
question  was  at  once  suggested,  Is  the  ratio  of  the 
atomic  weight  of  oxygen  and  hydrogen  in  fact  that 
of  16:  1.0025,  as  the  general  average  of  all  trust- 
worthy determinations  hitherto  made  seemed  to  in- 
dicate ;  or  was  there  a  constant  error  lurking  in 
these  results,  which  caused  the  very  slight  variation 
from  the  ratio  from  16  to  1  required  by  the  theory? 
I  must  confess  that  as  I  looked  at  the  proportion  as 
drawn  out  above,  the  conviction  pressed  upon  me 
that  this  variation  from  the  theory  must  be  apparent, 
and  I  determined  to  ferret  out  the  hidden  error  if 
possible. 

The  problem  was  easily  stated,  but  as  is  usual  in 
questioning  Nature,  her  answer  was  not  so  easily  in- 
terpreted, and  it  has  required  several  years  of  work 
to  reach  a  definite  conclusion.  The  results  were  at 
first  baffling,  and  it  was  not  until  grave  experimental 
difficulties  had  been  overcome  that  definite  conclu- 
sions could  be  reached ;  and  these  conclusions  were 
quite  different  from  what  had  been  anticipated.  It 
is  because  this  investigation  is  a  good  example  of 
the  methods  of  science,  and  an  illustration  drawn 
from  personal  experience  of  the  general  subject  we 


136  FORMER   INVESTIGATIONS. 

are  discussing,  that  I  venture  to  ask  your  attention 
to  some  of  its  details. 

On  studying  the  methods  by  which  the  ratios  of 
the  atomic  weights  of  oxygen  and  hydrogen  had 
been  determined,  it  was  evident  that  they  could  be 
divided  into  two  classes :  first,  the  direct  methods  of 
determining  the  ratio,  in  which  the  proportions  of 
oxygen  and  hydrogen  uniting  to  form  water  were 
actually  weighed  ;  secondly,  the  confirmatory  methods, 
to  whose  results  small  value  could  be  assigned  inde- 
pendently of  the  first.  Disregarding  the  last,  as  yield- 
ing no  conclusive  evidence  on  the  question  at  issue, 
it  appeared  that  all  the  trustworthy  determinations 
had  been  made  by  essentially  the  same  chemical 
process.  This  process  consists  in  burning  an  unde- 
termined amount  of  hydrogen  by  means  of  oxide  of 
copper,  and  weighing  the  water  which  results,  and 
further  determining  the  amount  of  oxygen  combined 
from  the  loss  of  weight  of  the  oxide  of  copper. 

The  chemical  process  is  a  very  simple  one.  Oxide 
of  copper  is  a  compound  solely  of  copper  and 
oxygen,  and  when  hydrogen  gas  is  passed  over  the 
heated  oxide  it  takes  up  the  oxygen  to  form  water, 
and  the  copper  is  left  in  the  metallic  state. 

By  weighing  the  glass  tube  containing  the  oxide 
before  and  after  the  experiment,  we  can  determine 
the  weight  of  oxygen  which  has  combined  with  the 
hydrogen ;  and  by  collecting  the  water  formed,  in 
appropriate  desiccators,  which  are  also  "weighed  be- 
fore and  after  the  experiment,  we  can  find  the  weight 
of  this  sole  product  of  the  process,  with  extreme 
accuracy. 


NECESSARY   CONDITIONS.  1 37 

By  subtracting  now  the  weight  of  the  oxygen 
found,  from  the  weight  of  the  water  found,  we  have 
the  weight  of  the  hydrogen  which  has  combined  with 
the  oxygen  in  the  process ;  and  the  proportion  be- 
tween the  weight  of  the  oxygen  and  the  weight  of 
the  hydrogen  is  one  half  of  the  atomic  ratio  we 
are  seeking;  because,  according  to  our  theories,  one 
atom  of  oxygen  combines  with  two  atoms  of  hydro- 
gen to  form  one  molecule  of  water. 

The  proportion  by  weight  in  which  hydrogen  com- 
bines with  oxygen  to  form  water  is  about  that  of  1 
to  8.     The  atomic  ratio  about  that  of  1  to  16. 

Considering  now  the  observed  ratio  of  1  to  8,  it  can 
be  seen  that  the  highest  accuracy  demands  that  each 
term  of  the  proportion  should  be  determined  to  an 
equal  degree  of  exactness.  Thus,  if  in  a  given  ex- 
periment we  have  8  grams  of  oxygen  uniting  with 
1  gram  of  hydrogen,  it  is  of  no  avail  to  weigh  the 
oxygen  to  a  tenth  of  a  milligram,  unless  we  can 
weigh  the  hydrogen  to  the  same  proportionate  de- 
gree of  accuracy;  for  an  error  9-10  of  a  milligram  in 
the  weight  of  the  water,  or  of  8-10  of  a  milligram  in 
the  weight  of  the  oxygen,  will  have  no  more  influence 
on  the  resulting  ratio  we  are  seeking  than  an  error  of 
1-10  of  a  milligram  in  the  weight  of  the  hydrogen. 
Remembering  now  that  1-10  of  a  milligram  is  about 
the  extreme  limit  of  accuracy  of  our  best  balances, 
when  loaded  with  more  than  a  few  grams  of  material, 
it  can  easily  be  seen  that  there  is  an  obvious  source 
of  error  in  the  determination  we  have  described. 

The  weights  actually  observed  are,  first,  that  of  the 
water  formed,  and  secondly,  that  of  the  oxygen  used. 


138  SOURCE  OF  ERROR. 

The  weight  of  »the  water  can  be  determined  to  within 
a  few  tenths  of  a  milligram ;  that  is,  with  all  the 
accuracy  with  which  our  problem  requires  that  the 
larger  term  of  the  proportion  8  to  1  should  be 
known ;  and  for  the  moment  this  weight  may  be 
regarded  as  established. 

It  is  quite  different  with  the  weight  of  the  oxygen ; 
this  last  is  found  by  weighing  the  glass  tube  contain- 
ing oxide  of  copper,  before  and  after  the  experiment, 
and  between  the  two  weighings  the  tube  is  heated  to 
a  low  red  heat  for  several  hours,  while  a  stream  of 
hydrogen  gas  is  passing  through  it;  and  there  are 
several  causes  which  might  lead  to  a  slight  variation 
in  these  weights,  independently  of  the  loss  of  oxygen, 
which  has  been  used  up  in  the  process.  It  is  un- 
necessary to  discuss  here  what  these  causes  are,  but 
their  effect  would  be  unimportant  if  they  only  led 
to  a  small  error  in  the  observed  weight  of  the  oxygen. 
Unfortunately,  this  is  not  the  case;  for  when,  in  order 
to  find  the  weight  of  the  hydrogen,  we  subtract  from 
the  weight  of  the  water,  accurately  known,  the  weight 
of  the  oxygen  —  which  maybe  for  the  causes  referred 
to,  slightly  erroneous  —  the  whole  error  appears  in 
the  weight  of  the  hydrogen  thus  found,  and  in  the 
opposite  direction.  If,  for  example,  the  weight  of 
the  oxygen  is  too  large,  the  weight  of  the  hydrogen 
will  be  too  small  by  exactly  the  same  amount ;  and 
although  the  error  may  be  an  inconsiderable  part  of 
the  weight  of  the  oxygen,  it  may  be  a  very  appre- 
ciable quantity  in  the  weight  of  the  hydrogen. 

On  the  other  hand,  if  a  means  could  be  devised  for 
weighing  the  hydrogen,  leaving  the   oxygen   to   be 


DUMAS'S   REMARKS.  1 39 

determined  by  subtracting  this  smaller  weight  from 
the  weight  of  the  water,  then  a  small  error  in  the 
observed  weight  of  the  hydrogen  would  have  no 
appreciable  effect  on  the  weight  of  the  oxygen. 

Professor  Dumas,  who  made  by  far  the  most  ex- 
tended series  of  observations  by  the  old  method, 
fully  recognized  the  source  of  error  to  which  I  have 
referred,  and  in  his  paper  on  the  subject  wrote  as 
follows :  — 

"  Of  all  analyses  which  a  chemist  can  undertake, 
that  of  water  is  the  one  which  offers  the  greatest  un- 
certainty. In  fact,  one  part  of  hydrogen  unites  with 
eight  parts  of  oxygen  to  form  water;  and  nothing 
would  be  more  exact  than  the  analysis  of  water,  if 
we  could  weigh  the  hydrogen  as  well  as  the  water 
which  results  from  its  combustion. 

"  But  the  experiment  is  not  possible  under  this 
form.  We  are  obliged  to  weigh  the  water  formed 
and  the  oxygen  used  to  produce  it,  and  to  calculate 
the  weight  of  the  hydrogen  consumed  in  the  process 
from  the  difference  of  these  two  weights.  Thus  an 
error  of  1-900  in  the  weight  of  the  water,  or  of  1-800 
in  the  weight  of  the  oxygen,  affects  the  weight  of  the 
hydrogen  by  a  quantity  equal  to  1-90  or  1-80  of  its 
value.  As  these  errors  are  in  the  same  direction 
they  are  added  to  each  other,  and  we  shall  have  an 
error  amounting  to  1-40." 

On  entering  upon  the  investigation  it  was  evident 
from  the  outset  that  no  advantage  was  to  be  gained 
by  multiplying  determinations  by  the  old  methods. 
The  work  had  repeatedly  been  done  by  the  best 
masters  of  the  science,  with  all  the  accuracy  of  which 


140  WEIGHING  A   GAS. 

the  method  was  capable.  The  only  hope  of  improve- 
ment lay  in  finding  some  method  of  weighing  the 
hydrogen  with  sufficient  accuracy;  and  it  was  essen- 
tial to  determine  this  weight  to  within  1-10,000,  or 
at  least  1-5000  of  its  value. 

A  gas  can  only  be  weighed  by  enclosing  it  in  a 
glass  globe  or  some  similar  receiver,  and  hydrogen 
is  so  exceedingly  light  that  its  total  weight  can  only 
be  a  very  small  fraction  of  the  containing  vessel ; 
moreover,  as  the  buoyancy  of  the  air  is  fourteen  and 
one  half  times  as  great  as  the  weight  of  the  hydrogen, 
the  variations  in  buoyancy  caused  by  changes  in  at- 
mospheric conditions  have  an  all-important  effect  in 
the  apparent  weight.  The  late  Professor  Regnault, 
of  Paris,  devised  a  very  ingenious  method  of  com- 
pensation which  could  readily  be  applied  in  this  case. 
It  consisted  in  balancing  the  globe  containing  the 
hydrogen,  hung  to  one  arm  of  the  balance,  by  a  sec- 
ond globe  of  exactly  the  same  volume  and  made  of 
the  same  material,  hung  to  the  opposite  arm,  and  so 
arranging  the  balance-case  that  both  globes  should 
hang  in  the  same  enclosure  and  therefore  be  equally 
affected  by  atmospheric  changes.  This  method  I 
applied  in  the  problem  before  us,  and  after  a  number 
of  trials  I  found  it  possible  to  make  the  compensation 
so  accurate  that  the  weight  of  my  globe  holding 
five  litres  of  gas  did  not  vary  more  than  1-10  of  a 
milligram  through  large  changes  of  temperature  and 
pressure.  In  order  now  to  weigh  the  hydrogen  with 
this  degree  of  accuracy,  it  was  only  necessary  to  ex- 
haust the  air  from  the  glass  receiver,  and  after  bal- 
ancing it  as  described,  to  fill  it  with  hydrogen,  when 


METHOD   OF  BURNING.  141 


the  increased  weight  (only  about  4-10  of  a  gram 
with  my  apparatus)  was  the  weight  of  the  hydrogen 
required. 

In  order  to  burn  this  hydrogen  I  used  essentially 
the  same  apparatus  as  previous  experimenters,  pas- 
sing the  gas  over  heated  oxide  of  copper,  collecting 
the  water  formed,  and  determining  its  weight.  Every 
detail  of  the  apparatus  was  the  result  of  careful  con- 
sideration, and  in  many  cases  was  only  reached  after 
numerous  experiments. 

There  were  many  difficulties  to  be  overcome,  but 
the  result  left  nothing  to  be  desired,  and  thus  far  the 
method  was  as  perfect  as  the  conditions  required. 

Everything  now  turned  upon  introducing  into  our 
globe  absolutely  pure  hydrogen,  and  here  the  great- 
est difficulties  were  met. 

Fortunately  at  this  point  I  secured  for  my  work 
the  assistance  of  a  young  chemist,  Mr.  T.  W.  Rich- 
ards, my  former  pupil  and  present  assistant,  of  whose 
experimental  skill  I  can  speak  as  warmly  as  did  Du- 
mas of  Stas. 

A  part  of  the  difficulties  of  filling  the  globe  with 
pure  hydrogen  were  wholly  mechanical,  and  the  only 
ones  which  it  is  important  I  should  mention  here  are 
the  difficulties  we  met  in  procuring  absolutely  pure 
gas. 

It  will  be  obvious  that  an  exceedingly  small  amount 
of  impurity  would  be  fatal  to  the  accuracy  of  my 
method.  If  the  hydrogen  we  introduced  into  our 
globe  carried  with  it  only  1-10,000  part  of  its  volume 
of  atmospheric  air,  —  an  impurity  which  it  is  exceed- 
ingly difficult  to  avoid,  on  account  of  the  rapid  dif- 


142  EFFECT   OF   SLIGHT   IMPURITY. 

fusion  of  hydrogen  and  the  pervasiveness  of  our 
atmosphere, —  this  impurity  would  increase  the  appar- 
ent weight  of  the  hydrogen  by  i-io  of  a  per  cent,  and 
cause  an  error  that  would  be  fatal  to  the  degree  of 
accuracy  we  were  seeking. 

In  our  earlier  determinations  we  drew  the  hydrogen 
gas  from  a  large  self-acting  generator  charged  with 
sulphuric  acid  and  zinc.  We  used  in  the  generator 
pure,  but  not  the  purest  materials,  which  it  would 
not  have  been  practicable  to  procure  on  the  scale  on 
which  we  then  expected  to  work ;  and  we  trusted  to 
a  complicated  system  of  purifiers  to  remove  the 
traces  of  sulphurous  oxide  or  other  chance  impuri- 
ties which  the  gas  might  contain.  With  hydrogen 
thus  prepared  and  purified,  we  made  a  large  number 
of  determinations.  We  give  only  a  few  of  these  in 
the  table  below,  but  those  here  exhibited  are  a  fair 
specimen  of  the  whole.  In  each  case  the  numbers 
express  the  atomic  weight  of  oxygen  referred  to 
hydrogen  as  unity ;  and  it  will  be  noticed  that  these 
values  are  not  only  far  below  the  average  of  the 
previous  results,  15.96,  but  also  that  they  differ 
widely  from  each  other. 

PRELIMINARY   RESULTS. 

15-793  !5-85°  I5-835 

15.790  15.937  I5-82o 

It  was  now  obvious  that  the  varying  values  must 
result  from  impurities  in  the  hydrogen,  and  as  we 
knew  that  our  purifiers  did  their  work  efficiently,  we 
were  persuaded  that  the  impurity  must  be  the  nitro- 
gen of  the  atmosphere  which  entered  our  apparatus 


FIRST   SERIES   OF   RESULTS.  143 


by  diffusion  at  its  many  joints.  We  sought  to  stop 
such  leaks  by  every  means  possible,  and  we  thus  suc- 
ceeded in  obtaining  better  and  better'  results,  but 
there  was  still  far  too  great  irregularity  to  make  the 
determinations  of  any  value,  and  we  were  finally 
forced  to  reduce  the  scale  of  our  experiments. 

We  then  constructed  an  apparatus  in  which  hydro- 
gen was  prepared  on  a  smaller  scale  from  chemically 
pure  zinc  and  hydrochloric  acid.  The  extent  of  the 
purifiers  was  greatly  reduced;  and  the  number  of 
joints  reduced  to  only  two  or  three,  and  these  were 
all  carefully  sealed  with  impervious  cement.  With 
this  apparatus  we  made  the  first  five  determinations 
given  in  the  table  on  page  148.  In  this  table  we 
give,  in  the  first  column,  the  weight  of  the  hydrogen 
burnt;  in  the  second  column,  the  weight  of  water 
obtained ;  in  the  third  column,  the  atomic  weight  of 
oxygen  deduced  from  these  weights  after  making 
allowance  for  the  buoyancy  of  the  air;  and  in  the 
last  column,  the  difference  between  each  atomic 
weight  and  the  average  of  the  five- 
It  will  be  seen  that  we  had  now  reached  a  very 
different  result.  All  the  values  are  closely  concord- 
ant, the  maximum  difference  from  the  average  cor- 
responding to  less  than  1-10  of  a  milligram  of  the 
hydrogen  weighed;  and  also  this  mean  value  very 
closely  agrees  with  15.96,  the  average  deduced  from 
previous  results. 

Indeed,  the  agreement  was  as  close  as  we  could 
possibly  expect.  If  there  was  an  error  it  could  not 
arise  from  any  fluctuating  cause,  like  the  diffusion  of 
air  which  we  had   previously  encountered ;    it  must 


144      SECOND   AND   THIRD   SERIES   OF   RESULT& 

be  some  constant  error  depending  on  the  process. 
Moreover,  we  felt  equally  sure  that  the  error,  if  any, 
could  not  arise  from  our  method  of  weighing  the 
hydrogen,  for  our  result  was  essentially  the  same  as 
that  obtained  by  the  older  process,  in  which  the  oxy- 
gen, and  not  the  hydrogen,  was  weighed.  Still,  to 
trace  out  any  error,  if  existing,  we  next  sought  to 
vary  the  process  of  preparing  the  hydrogen,  and  con- 
structed an  apparatus  with  equal  care  in  which  hydro- 
gen was  evolved  by  electrolysis,  that  is,  by  the  action 
of  a  current  of  electricity  on  a  mixture  of  water  and 
hydrochloric  acid.  With  the  gas  procured  from  the 
new  apparatus,  we  made  five  additional  determina- 
tions, which  follow  the  first  five  in  the  table  just  re- 
ferred to.  By  inspecting  the  column  of  differences, 
it  will  be  seen  that  the  concordance  in  this  second 
set  is  even  greater  than  in  the  first.  Apparently,  then, 
we  had  reached  a  maximum  which  we  could  not 
exceed  by  varying  the  process ;  but  that  there  might 
be  no  question  on  this  point,  we  set  up  an  apparatus 
still  simpler  than  the  last  two,  by  which  hydrogen 
gas  was  prepared  from  the  metal  aluminum,  and  a 
solution  of  caustic  potash ;  and  with  hydrogen  thus 
obtained,  we  made  still  five  other  determinations, 
whose  results  are  given  below  in  the  same  table. 
Here  again,  the  average  given  is  essentially  identical 
with  the  averages  of  the  other  two  series. 

The  evidence  now  seemed  to  be  conclusive;  the 
average  of  these  fifteen  experiments  must  be  the  true 
value  of  the  atomic  weight  of  oxygen,  within  a  very 
small  limit  of  probable  error.  The  process  had  been 
varied  in  every  conceivable  way,  and  with  the  same 


CONSTANT   ERROR   DISCOVERED.  145 

identical  result.  Nevertheless,  these  results  were 
affected  by  an  important  constant  error,  which,  al- 
though so  obvious  when  pointed  out,  had  been  over- 
looked in  spite  of  all  our  care.  The  publication 
above  referred  to  was  already  in  print  when  our 
attention  was  called  to  the  point  by  Lord  Rayleigh, 
who  had  been  working  on  a  similar  problem. 

In  adopting  the  method  of  Regnault  for  weighing 
the  hydrogen  gas  subsequently  burnt,  we  had  as- 
sumed with  this  eminent  physicist  that  the  volume 
of  the  globe  remained  invariable  after  the  air  had 
been  exhausted,  when  of  course  the  pressure  of  the 
air  on  the  exterior  surface  was  no  longer  balanced 
by  the  tension  of  the  gas  within.  As  Regnault  had 
himself  experimented  on  the  compressibility  of  glass, 
and  as  the  least  change  in  the  volume  of  the  ten 
litre  globe  which  he  used  must  have  most  seriously 
affected  the  values  he  obtained  for  the  densities  of 
the  aeriform  substances  on  which  he  experimented, 
—  namely,  air,  oxygen,  nitrogen,  hydrogen,  and  car- 
bonic acid,  values  which  have  since  been  regarded  as 
among  the  most  accurate  constants  of  science,  —  it 
seemed  safe  to  assume  with  him  that  the  effect  of  the 
atmospheric  pressure  on  the  globe  when  exhausted 
was  insensible.  And  it  should  be  remembered  that 
the  investigator  must  always  build  on  previous  work, 
and  that  there  could  be  no  progress  if  he  felt  obliged 
to  verify  all  the  data  which  he  necessarily  employs. 
He  must  accept  data  which  are  regarded  as  well- 
established,  and  in  selecting  these  data  he  is  neces- 
sarily guided  by  authority.  There  could  be  no 
better  authority  than  Regnault  on  the  point  in  ques- 


I46        AFFECTS  PREVIOUS  RESULTS. 

tion ;  his  results  have  been  hitherto  accepted  without 
question,  and  a  vast  amount  of  experimental  work 
has  been  based  upon  them. 

Nevertheless,  the  globe  which  Regnault  used  in 
his  determinations  of  gas  densities,  when  exhausted, 
must  have  been  sensibly  compressed  by  the  atmos- 
pheric pressure ;  and  must,  therefore,  have  appeared 
to  weigh  more  than  when  full  of  gas,  in  consequence 
of  the  diminished  displacement,  and  hence  the  less- 
ened buoyancy  of  the  atmosphere.  This  increase  of 
weight  must  have  been  about  1.29  milligrams  for 
every  cubic  centimeter  by  which  the  volume  of  the 
globe  was  compressed ;  and  the  observed  weights 
of  this  globe-full  of  the  different  gases  on  which 
Regnault  experimented  must,  therefore,  have  been 
too  small  by  the  same  quantity. 

Unless  the  globe  which  Regnault  used  has  been 
preserved  it  is  not  now  possible  to  correct  his  re- 
sults ;  since  the  amount  of  compression  of  a  glass 
vessel  under  a  constant  pressure  depends  on  condi- 
tions which  vary  widely  and  must  be  separately 
determined  for  each  vessel.  Fortunately,  in  our 
work  the  same  glass  globe  had  been  used  from  the 
first,  and  there  was  no  difficulty  in  determining  the 
exact  amount  by  which  our  results  had  been  influ- 
enced by  the  effect  under  discussion.  For  this  pur- 
pose it  was  only  necessary  to  weigh  the  globe  under 
water,  first  when  exhausted,  and  afterwards  when 
full  of  air.  Under  these  circumstances,  if  there  was 
any  change  of  volume,  the  difference  of  buoyancy 
would  become  very  marked,  and  could  be  accurately 
estimated. 


CORRECTION   FOUND.  1 47 

A  description  of  the  details  of  these  additional 
experiments  would  be  out  of  place  here.  It  is  suffi- 
cient to  say  that  the  shrinkage  of  the  glass  balloon 
we  used,  when  exhausted,  amounted  to  nearly  two 
cubic  centimeters,  or  about  0.0004  of  its  exterior 
volume;  that  in  each  of  our  determinations  the  true 
weight  of  the  hydrogen  gas  burnt  was  nearly  two 
milligrams  greater  than  the  apparent  weight;  and 
that  after  making  correction  for  this  altered  weight 
the  atomic  weight  of  oxygen  deduced  from  our  ex- 
periments is  15.869,  instead  of  15-953  as  before  given. 

After  such  a  catalogue  of  difficulties  encountered, 
and  errors  avoided,  it  may  well  be  asked,  How  can 
we  be  sure  that  there  may  not  be  still  other  causes 
of  constant  error  invalidating  our  results?  Obvi- 
ously we  cannot  be  sure.  All  we  can  do  is  to  work 
earnestly  and  conscientiously  for  the  truth,  and  leave 
the  future  to  revise  our  results  and  correct  our  mis- 
takes. In  this  way  the  truth  will  be  finally  reached, 
although  the  progress  may  be  slow  and  halting,  and 
our  individual  labor  may  appear  to  have  been  lost. 

But  although  the  exact  value  of  the  atomic  weight 
of  oxygen  may  hereafter  be  found  to  differ  more  or 
less  from  the  number  we  have  finally  reached,  the 
general  result  of  our  work  has  been  to  invalidate 
the  hypothesis  of  Prout.  This  theory  appears  to 
fail  at  the  most  critical  juncture.  Is  there  then  no 
significance  in  the  analogies  we  have  pointed  out? 
Has  the  close  approximation  of  the  ratios  of  so 
many  of  the  atomic  weights  to  a  proportion  between 
whole  numbers  no  meaning?  I  feel  persuaded  that 
there  is  a  significance  in  the  analogies,  and  a  mean- 


I48  TABLE   OF   RESULTS. 

ing  in  the  coincidences;  but  it  is  not  a  significance 
or  meaning  that  we  can  as  yet  interpret,  and  we  mu&t 
be  content  to  wait  for  more  knowledge  and  larger 
views. 

ATOMIC   WEIGHT   OF   OXYGEN. 

First  Scries. 

Weight  of  Hydrogen.  Weight  of  Water.  Atomic  Weight  of  Oxygen. 

0.4233  3.804S  15  977 

0.4136  3-7094  15-937 

0.4213  3.7834  15.960 

0.4163  3-7345  I5-94I 

0.4131  37085  15-954 


0.4112 
0.4089 
0.4261 
0.4197 
0.4144 


0.42205 
0.4284 
0.4205 
0.43205 

0-4I53 
0.4167 

15.952  ±0.0035 

Total  Average  15. 953  4-  0.0017'. 

After  correcting  for  shrinkage  of  balloon  under  the  atmos- 
pheric pressure,  — 

Final  result    .     .    .    15.869  ± 0.0017. 


15.954  4^  0  0048 

Second  Series. 

36930 

15.962 

3.6709 

15-955 

3-8253 

15-955 

3-7651 

15.942 

3-7I97 

15-953 

15.953  i  0.0022 

Third  Series. 

3-7865 

•5-943 

38436 

15.944 

3-777^ 

15.967 

3.8748 

15-937 

3.7281 

15-954 

3-7435 

15.967 

DEDUCTIONS  FROM  THE  LAW  OF  GRAVITATION.       1 49 

The  history  of  physical  astronomy  since  the  publi- 
cation of  the  "  Principia  "  furnishes  abundant  illustra- 
tions of  the  various  features  of  scientific  deduction  on 
which  we  have  dwelt  in  this  lecture.  There  has  been 
a  continuous  development  of  the  deductions  from  the 
law  of  gravitation,  and  in  this  work  the  mathematical 
genius  of  two  centuries  has  found  abundant  employ- 
ment. The  law  of  gravitation  is  one  of  the  few 
fundamental  principles  of  nature  of  which  we  feel 
confident  that  we  have  found  the  exact  expression. 
Most  of  the  laws  of  physical  science  are  only  laws  of 
approximation  ;  that  is,  laws  with  which  the  phe- 
nomena of  nature  closely  agree,  but  which  exhibit 
certain  discrepancies  that  lead  us  to  believe  that  with 
larger  knowledge  we  may  reach  more  accurate  repre- 
sentations of  the  truth.  But  the  law  of  gravitation 
appears  to  be  exact,  and  we  have  every  reason  to 
believe  that  in  the  progress  of  science  it  will  remain 
essentially  unaltered.  It  is,  moreover,  a  very  simple 
relation.  In  consequence  of  the  mode  of  action 
which  we  call  gravity,  and  which  is  as  mysterious  an 
agent  now  as  when  first  recognized,  a  pull  is  exerted 
between  any  two  masses  of  matter  in  the  universe,  or 
the  parts  of  any  two  masses,  which  is  proportional 
directly  to  the  products  of  the  two  masses,  and  in- 
directly to  the  square  of  their  distance  apart, —  as 
may  be  expressed  by  the  very  simple  algebraic 
formula: 

F MM' 

r —   £>2 

Unlike  any  other  physical  forces  with  which  we  are 
familiar,  this  attraction  is  not  influenced  by  the  na- 


150  PROBLEM   OF  THE  THREE   BODIES. 

ture  of  the  material  of  the  masses,  by  the  nature  of 
the  medium  interposed,  by  the  proximity  of  other 
masses,  or  by  any  other  conditions,  except  solely  the 
quantity  of  material  in  the  masses  and  the  distance 
between  them.  Newton  himself  made  these  points 
the  subject  of  an  experimental  investigation,  and  his 
results  have  been  confirmed  by  other  astronomers, 
who,  like  Gauss,  have  been  ready  enough  to  question 
the  finality  of  the  law ;  and  it  is  only  after  repeated 
doubts  have  been  resolved  in  its  favor  that  we  have 
settled  into  the  belief  that  it  is  precisely  correct. 
Still,  simple  as  the  law  is,  to  trace  its  action  between 
the  heavenly  bodies  becomes  at  once  a  problem  of 
great  difficulty. 

So  long  as  astronomers  limited  themselves  to  the 
question  of  central  forces  and  considered  only  the 
action  of  the  sun  on  the  individual  planets,  the  prob- 
lem was  comparatively  simple,  and  admitted  of  the  ele- 
gant solution  which  Newton  gave  in  the  "  Principia;  " 
but  when  the  universality  of  gravity  came  to  be  recog- 
nized, and  it  became  a  question  of  the  mutual  action 
and  reaction  of  all  the  bodies  in  the  universe,  not  only 
of  the  sun  on  the  planets  but  of  all  the  planets  on  each 
other,  the  problem  assumed  a  complication  with  which 
no  human  power  could  grapple,  and  whose  complete 
solution  was  impossible.  But  setting  aside  for  the 
time  the  more  general  problem  in  which  many  of  the 
forces  acting  were  so  slight  that  they  could  be  over- 
looked, there  was  in  the  fore-front  of  astronomy  the 
case  of  the  moon,  acted  on  strongly  by  both  the 
earth  and  the  sun ;  and  thus  arose  the  famous  prob- 
lem of  the  three  bodies,  which  alone  has  exhausted 


PLANETARY  PERTURBATIONS.        151 

the  powers  of  the  mathematicians  from  Newton's 
time  to  our  own.  When  only  three  bodies  simultan- 
eously attract  each  other  the  complication  of  effects 
is  so  great  that  only  approximate  calculations  are 
possible,  and  the  complete  solution  of  this  compara- 
tively simple  astronomical  problem  has  yet  to  be 
given.  Newton  himself  grappled  with  this  subject, 
and  so  far  succeeded  as  to  give  a  tolerably  accurate 
representation  of  the  moon's  motions ;  and  the  only 
open  bitterness  shown  during  his  life  appears  to  have 
been  displayed  towards  his  contemporary  Flamstead, 
the  first  Astronomer  Royal,  who  showed  unwilling- 
ness to  furnish  him  with  the  observations  he  needed 
to  compare  with  his  theory. 

The  consideration  of  the  mutual  attractions  of  the 
planets  and  the  sun  brings  us  to  the  more  complex 
problem  of  planetary  perturbations.  The  complete 
solution  of  this  problem  even  in  its  simplest  form  is 
hopeless,  and  the  principle  on  which  the  calculation 
of  planetary  perturbations  proceeds  is  to  reject  every 
effect  which  does  not  lead  to  a  quantity  appreciable 
in  observation.  The  quantities  thus  rejected  are 
indefinitely  more  numerous  and  complex  than  the 
few  larger  terms  which  are  retained ;  and  in  combin- 
ing these  last,  numerous  assumptions  have  to  be 
made  in  order  to  simplify  the  problem.  The  solution 
reached  therefore  is  merely  partial,  and  the  results 
approximate ;  but  by  such  tentative  methods  great 
perfection  has  been  reached  in  the  theory  of  the 
planetary  orbits. 

One  of  the  greatest  triumphs  of  astronomical  de- 
duction, and  yet  one  of  the  most  striking  illustrations 
11 


152  PERTURBATIONS   OF   URANUS. 

of  the  incompleteness  of  its  methods,  was  the  dis- 
covery of  the  planet  Neptune.  For  many  years  the 
observations  of  the  planet  Uranus,  discovered  by  the 
elder  Herschel  in  1781,  had  differed  markedly  from 
the  theory  of  its  orbit,  even  after  making  every  allow- 
ance for  the  perturbations  caused  by  its  nearest 
associates,  Saturn  and  Jupiter ;  and  what  was  more 
note-worthy,  the  error  had  gone  on  increasing  rapidly 
from  year  to  year.  That  this  effect  might  be  due  to 
the  disturbing  influence  of  an  unknown  outer  mem- 
ber of  the  solar  system  was  a  reasonable  supposi- 
tion; and  if  so,  the  theory  of  astronomy  ought  to 
be  able  to  predict  the  elements  of  the  orbit,  and, 
therefore,  to  point  out  at  any  moment  the  position  of 
the  disturbing  body.  Here,  however,  as  in  other 
problems  involving  the  mutual  action  of  several 
bodies,  a  complete  solution  was  impossible,  and  the 
tentative  methods  of  calculation  were  long  and  te- 
dious; so  that  astronomers  were  slow  to  undertake 
the  work.  But  in  1843  the  investigation  was  be- 
gun by  Adams  at  Cambridge,  England,  and  also,  at 
about  the  same  time,  by  Leverrier  at  Paris,  and  the 
issue  is  well  known. 

Leverrier  communicated  his  result  to  the  astrono- 
mer Galle,  by  a  letter  received  at  Berlin  September 
23,  1846;  and  the  same  evening  the  planet  was 
found,  nearly  in  the  place  pointed  out.  By  a  for- 
tunate coincidence,  a  map  of  that  portion  of  the 
heavens  —  one  of  the  sheets  of  Bremiker's  Berlin  star 
map,  then  recently  published  —  facilitated  the  search; 
and  Galle  quickly  found  a  star  of  the  eighth  magni- 
tude, not  on  the  map,  which  the  observations  of  the 


DISCOVERY   OF  NEPTUNE.  1 53 

next  two  days  showed  must  be  the  object  sought. 
A  year  previously,  however,  Adams  had  communi- 
cated to  Professor  Challis  of  the  Cambridge  Observa- 
tory, the  results  of  his  independent  calculation,  which 
subsequently  proved  to  correspond  closely  with  those 
of  Leverrier;  but  although  search  had  been  made, 
and,  as  afterwards  appeared,  the  planet  had  been 
seen,  it  had  not  been  recognized  from  want  of  such 
a  map  as  the  Berlin  astronomer  possessed. 

Thus  two  separate  mathematicians,  without  concert 
with  each  other,  reached  the  same  solution  of  this 
difficult  problem,  and  their  prediction  appeared  to  be 
precisely  verified.  Could  there  be  a  more  striking 
confirmation  of  theory,  a  greater  achievement  of 
human  intellect?  And  yet  in  its  greatest  triumph 
mathematical  analysis  displayed  its  weakness. 

On  March  16,  1847,  within  six  months  of  the  dis- 
covery of  the  new  planet,  Professor  Benjamin  Peirce 
stated  to  the  American  Academy  of  Arts  and  Sci- 
ences, in  words  which  I  quote  from  their  Proceed- 
ings, "  The  planet  Neptune  is  not  the  planet  to 
which  geometrical  analysis  has  directed  the  tele- 
scope." This  declaration,  first  received  with  distrust, 
proved  to  be  fully  justified.  The  planet  of  the  theory 
had  a  mean  distance  from  the  sun  of  from  35  to  37.9 
times  that  of  the  earth,  with  a  corresponding  period 
of  revolution  of  from  207  to  233  years.  The  actual 
Neptune  has  a  mean  distance  of  only  30,  with  a 
period  of  about  168  years.  At  the  time  of  the  dis- 
covery, the  planet  of  the  theory  and  the  actual 
Neptune  had  approximately  the  same  apparent  posi- 
tion, or,   as    astronomers   say,  were    in    conjunction. 


154  HAPPY   ACCIDENT. 

But  this  was  a  "  happy  accident,"  and  to  this  chance 
the  discovery  of  the  actual  planet  must  be  ascribed. 

As  Professor  Peirce  clearly  showed  at  the  time, 
this  singular  result  depended  on  the  approximate 
and  tentative  character  of  the  method  of  calculation 
necessarily  employed.  Had  the  conditions  been  ex- 
actly known,  and  had  the  mathematical  analysis  been 
exhaustive,  the  actual  planet  which  caused  the  per- 
turbations would  doubtless  have  been  at  once  pointed 
out;  but  several  approximate  solutions  of  the  prob- 
lem were  possible.  Of  these  the  theoretical  planet 
was  one,  the  actual  planet  was  a  second,  and  still 
others  might  be  distinguished. 

The  problem  could  not  be  approached  without 
making  an  assumption  in  regard  to  the  solar  dis- 
tance, and  as  both  mathematicians  were  led,  by  the 
so-called  law  of  Bode,  to  make  the  same  assumption, 
they  came  to  the  same  approximate  result.  Unfortu- 
nately, the  law  assumed  to  regulate  the  relative  dis- 
tances of  the  planets  from  the  sun  conspicuously 
failed  in  the  case  of  Neptune,  and  we  have  heard  but 
little  of  it  since.  According  to  this  law,  the  solar 
distance  of  Neptune  should  have  been  about  39.6 
times  the  earth's  distance.  Leverrier  tried  successive 
assumptions,  beginning  with  39.1,  and  finding  that 
with  a  diminishing  value  the  conditions  of  the  prob- 
lem were  at  first  better  satisfied,  while  afterwards  the 
discrepancies  increased,  he  concluded  that  the  value 
must  be  within  the  limits  stated  above.  Adams 
followed  in  part  the  same  course,  although  his  cal- 
culations were  less  full.  The  planet  found  had  a 
distance  of  30  only,  and  if  the  calculations  had  been 


METHOD   OF   CALCULATION.  155 


extended  to  this  limit,  another  solution  of  the  prob- 
lem would  have  appeared  which  proved  to  be  the 
true  one.  But  the  second  solution  was  not  suspected ; 
because  at  an  assumed  distance  of  35.3  there  was  a 
singular  point  which  introduced  peculiar  disturbances. 
In  a  word,  the  theoretical  planet  was  an  approximate 
solution  of  the  problem  for  the  field  of  research  cov- 
ered by  the  analysis ;  while  the  real  planet  was  out- 
side of  this  field,  and  separated  from  it  by  a  barrier 
which  the  partial  analysis  could  not  overstep. 

You  cannot  find  in  the  whole  history  of  science  a 
more  striking  illustration  than  this,  both  of  the  power 
and  of  the  limitations  of  deductive  thought.  The  dis- 
covery of  a  new  planet  appeals  strongly  to  the  imagi- 
nation of  men ;  and  the  story  of  the  mathematician 
who  from  his  study  directed  the  astronomer  where  to 
find  a  predicted  member  of  the  solar  system,  is  con- 
stantly told  as  an  evidence  of  intellectual  power,  —  less 
frequently  as  a  signal  instance  of  mental  limitations 
and  human  fallibility;  and  yet  the  last  is  the  more 
impressive  lesson.  Here,  however,  as  so  often  in 
human  affairs,  weakness  was  made  strength.  Through 
striving,  the  planet  was  discovered  and  the  boundaries 
of  knowledge  were  extended. 

Obviously  there  was  a  large  element  of  chance,  or 
—  as  I  prefer  to  call  it —  Providence,  in  the  discovery 
of  Neptune ;  and  such  chances  have  been  repeatedly 
the  turning-points  in  the  history  of  science.  The 
accidental  breaking  of  a  crystal  of  Iceland  spar  re- 
vealed to  Hawy  the  structure  of  crystalline  bodies. 
A  chance  reflection  of  light  from  the  windows  of  the 
Luxembourg  Palace  in  Paris  disclosed  to  Malus  the 


156  RESULTS   OF  CHANCE. 


laws  of  polarization.  The  twitching  of  the  legs  of  a 
frog  first  made  known  to  Galvani  the  existence  of  low 
tension  electricity.  The  swing  of  a  compass-needle 
on  his  lecture-table  opened  to  Oersted  the  phenomena 
of  electro-magnetism,  and  was  the  simple  beginning 
from  which  have  come  all  the  wonderful  applications 
of  electrical  currents.  In  the  remark  that  Lagrange 
is  said  to  have  made  of  Newton,  that  "  such  accidents 
happen  only  to  those  who  deserve  them,"  there  is  a 
deeper  philosophy  than  was  probably  intended.  It 
must  be  remembered  that  to  a  higher  intelligence 
there  can  be  no  such  thing  as  accident;  and  that 
"  the  fortuitous  concourse  of  atoms,"  like  any  other 
event,  would  be  seen  to  have  its  antecedents  and 
causes  if  our  imperfect  perceptions  could  take  cog- 
nizance of  their  existence.  Moreover,  even  on  our 
plane,  numbers  would  fail  to  convey  a  conception  of 
the  utter  hopelessness  of  the  chance,  on  the  doctrine 
of  probabilities,  that  the  right  accident  would  happen 
to  the  right  man  at  the  right  time. 

On  the  other  hand,  such  experience  as  I  have 
narrated  should  show  us  that  close  coincidences  of 
approximate  results  are  in  themselves  no  sure  test  of 
truthfulness,  and  carry  with  them  but  little  weight. 
Men  of  science  are  familiar  with  this  principle,  and 
almost  every  investigator  could  enforce  it  by  numer- 
ous examples.  But  on  most  men  such  coincidences 
make  an  extraordinary  impression ;  and  many  of  the 
delusions  of  society,  including  the  astrology  of  the 
past  and  the  pseudo-spiritualism  of  the  present,  find 
their  chief  support  in  the  apparent  coincidences  which 
a  wide  latitude  of  variation  permits. 


COINCIDENCES    OFTEN   ILLUSORY.  1 57 

Lastly,  such  experience  should  teach  us  how  unsafe 
it  is  to  rely  implicitly  on  popular  statements  of  scien- 
tific deductions.  An  impression  widely  prevails  that 
however  important  a  knowledge  of  the  general  results 
of  science  may  be,  it  is  not  necessary  that  the  literary 
man  or  the  general  scholar  should  acquaint  himself 
with  scientific  methods.  But  it  is  obvious,  from  what 
has  been  said,  that  no  accurate  knowledge  of  the  facts 
of  nature  is  possible  without  a  knowledge  of  the 
methods  by  which  the  facts  have  been  established. 
The  phenomena  of  nature  are  so  complex,  and  the 
simplest  effects  so  modified  by  concurring  agencies, 
that  they  cannot  be  fully  comprehended  unless 
studied  in  their  natural  relations.  The  phenomena 
described  in  text-books  are  often  not  realities  of 
nature,  but  ideal  relations  which  are  as  much  abstrac- 
tions as  the  conceptions  of  geometry.  As  systems 
of  science  such  books  have  their  value;  but  their 
necessarily  general  statements  are  not  often  a  sound 
basis  for  theological  arguments.  We  cannot  safely 
reason  from  the  facts  of  nature  until  we  know  them 
with  all  their  limitations ;  and  if  I  have  enabled  you 
to  realize  this  truth,  my  chief  object  in  this  lecture 
has  been  gained. 


158      INDUCTION   AND   DEDUCTION   CONTRASTED. 


LECTURE    VI. 

LAWS    OF   NATURE. 

TN  the  previous  lectures  we  have  endeavored  to 
■*■  make  clear  the  distinction  between  induction  and 
deduction  in  scientific  investigation.  Induction  is  the 
discernment,  recognition,  and  verification  of- a  general 
principle  of  nature  previously  unknown.  The  dis- 
cernment may  be  more  or  less  accurate,  the  recogni- 
tion more  or  less  satisfactory,  the  verification  more 
or  less  complete ;  but  the  process  is  essentially  an 
intuitive  act  of  the  mind  working  upon  previous 
knowledge  or  experience,  and  familiar  acquaintance 
with  natural  phenomena.  Hence,  under  favorable 
conditions,  it  is  more  or  less  spontaneous,  and  cannot 
be  regulated  by  methods  or  directed  by  rules.  It  is, 
in  a  word,  the  product  of  genius. 

Deduction  is  the  evolution  by  logical  processes, 
mathematical  or  otherwise,  of  the  consequences,  in- 
ferences, or  implications  which  a  general  principle 
includes  or  suggests.  It  may  be  more  or  less  direct, 
more  or  less  difficult,  more  or  less  exhaustive ;  but  in 
any  case  the  results  were  implicitly  involved  in  the 
premises  established  or  assumed.  It  is  a  creature  of 
methods,  a  slave  to  rules,  and  deals  with  syllogisms, 
equations,  observations,  experiments,   and   measure- 


OPINION   OF  JEVONS.  1 59 

ments  of  every  kind.  It  is  the  task  of  the  many,  the 
work  of  the  great  army  of  scientific  laborers. 

Induction  raises  the  level  of  human  knowledge; 
deduction  expands  that  knowledge.  Induction  opens 
new  fields  of  investigation ;  deduction  explores  these 
fields.  Induction  discloses  hidden  treasures  ;  deduc- 
tion appropriates  and  uses  them.  Induction  soars; 
deduction  creeps.  Induction  aspires  ;  deduction  con- 
templates. Induction  is  imaginative;  deduction  is 
realistic.  Induction  is  theoretical;  deduction  is  prac- 
tical. Induction  is  bold  and  confident;  deduction  is 
cautious  and  sceptical. 

I  am  well  aware  that  the  position  I  have  taken 
is  not  wholly  in  harmony  with  the  mechanical  view 
of  induction  which  the  authority  of  Bacon  has  so 
strongly  impressed  on  English  thought;  but  I  still 
feel  confident  that  I  am  in  sympathy  with  the  great 
body  of  scholars  who  are  practically  familiar  with 
scientific  methods. 

Professor  Jevons,  who  as  a  logician  classified  in- 
duction as  inverse  deduction,  thus  wrote  in  regard  to 
the  nature  of  the  process  itself:  "All  induction  is 
but  the  inverse  application  of  deduction ;  and  it  is  by 
the  inexplicable  mental  action  of  a  gifted  mind  that  a 
multitude  of  heterogeneous  facts  are  caused  to  range 
themselves  in  luminous  order  as  the  results  of  some 
uniformly  acting  law."  This  is  the  best  authority  I 
could  quote  ;  and  I  now  pass  on  to  consider  certain 
distinctions  among  the  results  of  induction,  which 
I  hope  will  serve  to  make  our  conceptions  of  the 
subject  still  clearer. 

Of  all  the  results  of  induction  there  are  none  so 


160  LAWS   OF  NATURE   DEFINED. 

familiar  or  so  striking  as  the  laws  of  nature ;  and  of 
the  aspects  of  the  material  universe  there  is  none 
which  is  more  appalling  to  the  religious  mind  than 
the  reign  of  law.  Law  and  Providence  seem  incom- 
patible and  mutually  exclusive.  "  The  wind  bloweth 
where  it  listeth,"  without  regard  to  the  tempest-tossed 
ship  freighted  with  the  hopes  of  nations.  The  laws 
of  motion  do  not  spare  precious  lives  when  a  broken 
rail  turns  the  rushing  train  from  its  appointed  track. 
The  law  of  gravitation  made  no  discrimination  among 
the  victims  on  whom  the  Tower  of  Siloam  fell ;  and 
so  fire  and  flood,  pestilence  and  famine,  tornado  and 
earthquake,  have  ever  involved  the  good  and  the  bad 
alike  in  common  ruin. 

Law  is  inexorable,  cruel,  pitiless ;  and  no  wonder 
that  as  thus  viewed  the  conception  of  law  should  be 
a  hindrance  to  faith.  But  this  view  of  nature  is  a 
misconception  which  arises  from  a  superficial  knowl- 
edge of  the  facts ;  and  the  law  of  the  text-books,  or 
of  the  popular  imagination,  is  for  the  most  part  an 
ideal  phantom.  Correct  views  on  this  subject  are  of 
such  supreme  importance  in  natural  theology  that  I 
propose  to  devote  two  lectures  to  a  discussion  of  some 
of  the  distinctive  features  and  manifold  variations 
which  the  so-called  laws  of  nature  present. 

A  law  of  nature  is  simply  a  declaration  or  state- 
ment of  a  certain  order,  sequence,  or  relation,  observed 
among  material  phenomena.  Jevons  says,  "  The  laws 
of  nature  are  simply  general  propositions  concerning 
the  correlation  of  properties  which  have  been  found 
to  hold  true  of  bodies  hitherto  observed."  And 
again:   "A  law  of  nature  is  not  a  uniformity  which 


LAWS   OF  NATURE  NOT   EFFICIENT   CAUSES.      l6l 

must  be  obeyed  by  all  objects;  but  merely  a  uni- 
formity which  is,  as  a  matter  of  fact,  obeyed  by  those 
objects  which  have  come  beneath  our  observation." 
Thus  the  first  law  of  motion  declares  that  any  mass 
of  matter  continues  in  its  state  of  rest  or  motion  until 
acted  on  by  some  force  external  to  itself.  The  law 
of  Mariotte  affirms  that  the  volume  of  a  given  mass 
of  gas  is  inversely  proportional  to  its  tension.  The 
law  of  gravitation  states  that  any  two  masses  of  matter 
attract  each  other  with  a  force  directly  proportional 
to  the  product  of  the  two  masses,  and  inversely  pro- 
portional to  the  square  of  the  distance  between  them  ; 
and  so  we  might  multiply  examples.  Notice,  noth- 
ing is  affirmed  in  regard  to  the  mode  of  action  in 
either  case.  The  phenomena  observed  may  be  the  effect 
of  a  single  cause,  or  the  resultant  of  several  causes ; 
but  the  law  takes  no  cognizance  of  any  such  feature. 
It  only  recognizes  the  order,  sequence,  or  relations 
it  describes.  This  is  a  most  important  point,  to  which 
I  would  ask  your  special  attention. 

The  laws  of  nature  are  simply  statements  of  ob- 
served relations.  They  are  not  efficient  causes  or 
modes  of  action  of  any  kind;  and  whatever  features 
with  such  an  aspect  may  be  superimposed  upon  the 
formal  propositions  in  the  description  or  by  the  im- 
agination, is  something  superadded  to  their  only  real 
sanction  as  laws  of  nature. 

There  may  seem  to  be  in  the  statement  of  the  law 
of  gravitation,  as  usually  given  and  as  enunciated 
above,  something  conflicting  with  the  positive  position 
here  laid  down.  When  it  is  said  that  one  mass  of 
matter  attracts  another,  or,  as  Newton  himself  enun- 


1 62  "  HYPOTHESES   NON   FINGO." 

ciatcd  the  law,  every  particle  of  matter  in  the  universe 
attracts  every  other  particle,  it  might  appear  as  if  a 
mode  of  action  was  declared  in  the  proposition ;  and 
I  have  no  doubt  that  the  law  is  so  understood  by 
nine  out  of  ten  of  the  students  who  repeat  the  state- 
ment. But  Newton  intended  to  convey  no  such  con- 
ception ;  and  no  such  conception  was  received  by  the 
scholars  for  whom  he  wrote. 

It  is  true,  however,  that  one  mode  of  explaining 
the  law  is  to  assume  that  there  resides  in  the  ulti- 
mate particles  of  matter  some  unknown  virtue  which 
determines  the  attraction.  But  this  is  a  pure  hypo- 
thesis, one  of  those  redundancies  referred  to  above, 
for  which  the  law  must  not  be  held  accountable. 
When  Newton  himself  was  asked  whether  he  had  any 
conception  of  this  kind  he  is  said  to  have  replied : 
"  Hypotheses  non  fingo." 

Moreover,  the  whole  tendency  of  modern  science  is 
entirely  opposed  to  any  theory  which  assumes  an 
inherent  potency  in  the  particles  of  matter;  and,  in 
the  case  of  gravitation,  such  an  hypothesis,  as  we 
shall  see  in  the  next  lecture,  is  beset  with  insuperable 
difficulties  and  objections.  It  would  be  better  if  we 
could  enunciate  the  law  without  using  the  word  "  at- 
tract; "  but  this  cannot  be  done  without  an  awkward 
circumlocution.  Of  course  what  is  meant  is  simply 
that  two  bodies,  if  free  to  move,  would  act  as  if  they 
were  pulled  by  a  force  varying  according  to  the  well- 
known  law;  and  what  is  true  of  this  proposition  is 
equally  true  of  the  statement  of  every  recognized  law 
of  nature.  All  such  propositions  are  intended  to 
declare  solely  a  relation  between  -phenomena ;   and  in 


DANGER   OF   MISAPPREHENSION.  1 63 

any  case  if  the  language  implies  more,  there  is  some- 
thing accessory,  which  careful  criticism  will  distin- 
guish and  eliminate. 

When  such  propositions  are  briefly  enunciated  in 
ordinary  language  there  is  always  danger  of  misap- 
prehension and  confusion ;  and  hence  one  of  the 
objections  to  unguarded  popular  statements  of  scien- 
tific principles  to  which  I  have  referred.  For  instance, 
from  the  ordinary  statement  of  the  law  of  inertia  — 
every  mass  of  matter  continues  in  its  state  of  rest  or 
motion  until  acted  on  by  some  force — I  know  by 
experience  that  a  large  majority  of  students  derive 
the  idea  that  an  original  state  of  motion  must  have 
been  the  effect  of  some  force ;  and  yet  this  is  pre- 
cisely the  reverse  of  the  impression  that  the  words 
were  intended  to  convey ;  and  in  general  I  may  say 
that  it  is  rare  that  students  acquire  from  text-books 
on  physics  correct  conceptions  of  the  fundamental 
principles  of  mechanics. 

The  popular  conception  which  so  constantly  asso- 
ciates causation  with  a  law  of  nature  undoubtedly 
arises  from  the  figurative  use  of  the  word  law  in  this 
connection.  Law  in  human  relations  implies  a  law- 
giver; and  therefore  we  associate  with  human  laws 
the  personal  attributes  of  the  law-giver.  The  laws  of 
the  Medes  and  Persians  were  inflexible ;  the  laws  of 
the  Romans  were  equitable;  the  old  laws  of  England 
were  cruel ;  the  modern  English  laws  are  more  mer- 
ciful, —  simply  because,  each  and  all,  they  reflected 
the  character  of  the  men  who  made  and  administered 
them  ;  but  to  call  the  law  of  gravitation  pitiless  is 
like  calling  the  multiplication  table  inexorable,  or  a 


1 64  EVIL   AND   LAW. 


prisoner's  chains  cruel.  Of  course  it  will  be  said  such 
language  is  figurative;  but  the  difficulty  is  that  the 
distinction  between  the  figurative  and  the  real  is  not 
always  kept  clear ;  and  this  is  not  the  only  case  in 
which  mental  confusion  and  logical  fallacy  have 
arisen  from  the  use  of  familiar  terms. 

Still,  while  all  must  admit  that  the  definition  of  a 
law  of  nature  as  here  given  is  conformable  to  the 
best  usage  among  scientific  scholars,  it  may  be  said, 
the  awful  fact  remains  that  amidst  the  misfortunes  of 
man,  the  whole  aspect  of  external  nature  is  hard  and 
pitiless,  and  fine-drawn  distinctions  do  not  relieve 
the  suffering  that  the  relentless  march  of  natural 
phenomena  entails.  Certainly  not !  We  cannot  solve 
the  terrible  problem  which  the  evil  of  the  world 
everywhere  presents.  This  is  a  fact  of  nature,  as  well 
as  law.  But  do  not  confound  it  with  law.  Its  sources 
are  far  deeper,  among  those  hidden  springs  of  being 
whence  flow  also  the  equally  mysterious  relations  of 
personality  and  free  will.  Do  not  then  by  any  per- 
version of  thought  associate  malevolence  with  the 
laws  of  nature.  To  a  finite  being,  law  means  reliance, 
confidence,  and  repose.  It  is  heaven-born,  beneficent 
order;  but  it  has  no  potency  in  itself,  and  may  be 
used  by  the  powers  of  evil  as  well  as  by  the  powers 
of  good. 

Another  popular  misconception  of  the  relations  of 
a  law  of  nature  appears  in  the  trite  argument  so  often 
urged  as  a  disproof  of  the  Christian  miracles.  It  is 
impossible  to  conceive,  it  is  said,  that  a  law  of  nature 
should  be  broken.  Certainly  it  is,  and  so  it  is  im- 
possible  to    conceive   that   the  qualities  of  metallic 


CONSTANCY   OF   LAW.  165 


gold  should  be  changed.  Were  the  properties  of 
gold  changed  in  the  least  degree  the  material  would 
be  no  longer  gold ;  and  so,  were  the  relations  predi- 
cated by  the  law  of  gravitation  altered,  we  should  at 
once  have  a  different  law.  I  do  not  say  that  either 
of  these  changes  is  possible,  much  less  probable;  but 
I  do  maintain  that  they  are  both  conceivable,  and 
not  so  inconsistent  with  our  actual  knowledge  of  the 
order  of  nature  as  to  render  the  supposition  inhe- 
rently absurd.  So  far  from  this,  the  transmutation  of 
the  metals  was  the  favorite  problem  of  the  elder 
chemists ;  and  it  is  well  known  that  Sir  Isaac  New- 
ton, whose  scientific  sobriety  cannot  be  questioned, 
devoted  a  great  deal  of  time  to  experiments  in  this 
direction;  and,  although  in  a  somewhat  different 
form,  the  question  has  been  reopened  in  our  own 
day.  So  also,  as  before  said,  the  most  eminent  men 
of  science  have  seriously  considered  whether  the 
law  of  gravitation  might  not  be  modified  under  new 
conditions. 

Could  each  law  be  traced  to  a  single  definite  cause, 
it  is  obvious  that  a  change  in  the  law  would  imply  a 
corresponding  change  in  the  cause,  and,  therefore  an 
alteration  of  purpose,  or  method,  inconsistent  with 
our  philosophy  either  of  an  intelligent  first  cause  or 
even  of  a  self-evolving,  self-sustained  cosmogony. 
But  these  are  not  the  conditions.  The  laws  of  nature 
are  relations  of  phenomena  which,  in  most  cases,  at 
least,  are  obviously  resultants  of  many  causes  whose 
action  is  inextricably  commingled ;  and  it  is  perfectly 
possible  to  conceive  of  a  new  element  introduced 
into   one   of  the   chains   of  causation  which  would 


!66  CONSTANCY   OF   LAW. 


utterly  alter  the  final  result.  I  do  not  say  that  this  is 
possible  ;  but  I  do  say  that  we  have  no  positive  knowl- 
edge which  makes  such  a  contingency  impossible. 

Man  cannot  increase  by  the  smallest  fraction  either 
the  material  or  the  energy  he  employs ;  but  he  can 
introduce  conditions  into  the  chain  of  causation,  by 
which  he  is  able  to  control  and  determine  events,  and 
even  to  alter  the  face  of  the  earth.  Why,  then,  may 
not  new  issues  appear  in  nature?  Why  may  not 
a  new  force  overrule  an  old  one?  Why  indeed  may 
not  unrecognized  agencies,  which  have  always  existed, 
and  whose  effects  have  been  slowly  accumulating,  at 
any  moment  appear  as  important  factors  in  human 
affairs  and  relations?  Not  only  do  I  see  no  reason 
for  believing  that  we  possess  an  exhaustive  knowl- 
edge of  nature's  powers  ;  but  on  the  contrary  I  am 
persuaded  that  even  in  the  most  familiar  fields,  there 
may  at  any  time  appear  indications  of  forces  hitherto 
undiscovered,  which  may  be  capable  of  momentous 
effects.  Remember  that  it  is  only  a  century  ago 
that  the  first  indications  were  noticed  of  a  power 
which  is  now  one  of  the  chief  agencies  of  our  civiliza- 
tion. And  what  were  these  indications?  Only  the 
momentary  twitching  of  a  frog's  legs  ! 

Let  it  be  understood  that  I  make  no  claim  to  sub- 
stantiate or  explain  miracles  ;  but  I  do  maintain  that 
we  cannot  disprove  Divine  interference  in  the  course 
of  nature  ;  and  that  the  scientific  probabilities  against 
such  occurrences  may  be  fairly  set  off  against  the 
moral  presumptions  in  their  favor.  To  me  it  seems 
to  be  a  question  of  evidence,  upon  which  our  knowl- 
edge of  the  laws  of  nature  has  no  bearing.     More- 


"SPIRITUAL   MANIFESTATIONS."  167 

over,  to  my  mind  the  marvellous  in  these  events  is  no 
weighty  evidence  against  their  credibility.  What  could 
be  more  marvellous  than  many  of  the  revelations  of 
modern  science?  As  I  distinctly  remember,  the  re- 
volving of  the  vanes  of  Crooke's  radiometer,  seemed 
to  me,  when  I  first  saw  the  instrument,  as  much  out 
of  the  ordinary  course  of  nature,  as  would  the  turning 
of  water  into  wine.  Investigation  showed  that  the 
motion  was  the  normal  result  of  a  force  which  had 
always  been  acting,  though  unsuspected ;  and  so  at 
any  moment  a  strange  phenomenon  may  put  us  in 
possession  of  a  new  force  which  will  overrule  all  the 
powers  of  the  world,  and  make  more  than  the  dreams 
of  Aladdin  sober  realities.  Nothing  is  too  marvellous 
to  be  believed,  provided  it  is  substantiated  by  satis- 
factory evidence. 

Why,  then,  it  may  be  asked,  do  you  not  believe  in 
mind-reading,  clairvoyance,  faith-cure,  and  other  so- 
called  spiritual  manifestations,  with  which  the  popu- 
lar mind  is  from  time  to  time  deluded?  Simply 
because  they  are  not  attested  by  satisfactory  evidence. 
It  is  upon  this  ground,  and  not  on  account  of  their 
strangeness  or  improbability,  that  we  hesitate  to  ac- 
cept them.  There  are  doubtless  facts,  and  very  in- 
credible facts,  concerning  these  matters,  that  are  well 
attested  ;  and  there  may  be  agencies  which  have 
never  been  recognized.  But  the  phenomena  claimed 
to  exist  are  so  complex,  and  so  obscured  by  uncon- 
scious self-deception,  or  by  actual  imposture,  that  no 
undoubted  truth,  or  definite  relation,  has  as  yet  been 
established. 

Societies  have  been  formed,  both  in  this  country 


1 68  GLOOMY  ASPECT   OF  NATURE. 

and  in  England,  for  the  promotion  of  psychical  re- 
search; but  it  may  be  questioned  if,  in  the  presence 
of  so  many  problems  of  nature  which  are  within  our 
grasp,  it  is  good  policy  to  expend  energy  on  those 
which,  for  the  time  at  least,  are  hopelessly  involved ; 
and  also  whether  it  is  wise  to  concentrate  public  at- 
tention on  abnormal  states,  or  diseased  conditions  of 
mind,  which  will  certainly  be  excited  and  spread 
thereby.  Nevertheless,  if  a  single  clearly  new  phe- 
nomenon were  elicited  by  such  investigations,  who 
can  question  that  it  would  be  studied  with  the  same 
zest  as  was  Crooke's  radiometer? 

Of  course  I  do  not  forget  the  paralyzing  impression 
of  desolation  and  despair  which  in  some  moods  the 
uniformity  of  nature  forces  on  the  mind;  but  this 
impression,  though  an  unquestionable  feature  of  hu- 
man experience  from  the  earliest  times,  has  no  per- 
tinency to  the  laws  of  nature.  This  aspect  of  nature 
affects  most  strongly  minds  of  an  imaginative  temper- 
ament, and  is  one  which  the  study  of  science  rather 
tends  to  soften  and  elucidate.  It  is  seen  as  clearly 
by  the  poet  as  by  the  philosopher;  and  it  inspires 
fatalism  more  often  than  scepticism.  It  is  a  part  of 
the  discipline  of  life,  to  which  all  sorts  and  conditions 
of  men  must  bow.  This  aspect  of  nature  has,  then, 
no  special  relations  to  our  scientific  knowledge ;  only 
the  facts  of  science  are  often  perverted  to  sustain  the 
terribly  gloomy  philosophy  it  suggests.  Moreover, 
science  has  pointed  out  the  one  consideration  which 
may  solve  the  mystery. 

The  insect's  life  is  often  only  a  summer's  day 
whose  sunshine  knows  no  change;    and  may  not  the 


babbage's  calculating  engine.  169 


uniformity  of  nature  during  human  life  be  like  a 
shifting  scene  to  Him  with  whom  we  have  to  do? 
Such  a  doctrine  is  wholly  consistent  with  our  knowl- 
edge of  the  laws  of  nature  ;  and  the  point  has  been 
so  forcibly  put  by  the  late  Charles  Babbage,  in  the 
"  Ninth  Bridgewater  Treatise,"  the  most  profound  of 
those  celebrated  works,  that  I  cannot  do  better  than 
to  quote  his  words.  After  describing  the  calculating 
machine,  which  is  so  inseparably  associated  with  his 
name,  and  showing  that  such  an  engine  might  work 
invariably  by  one  law  of  action,  during  any  finite 
number  of  steps  however  great,  and  yet  at  a  prede- 
termined point  introduce  a  break  in  the  series,  —  for 
instance,  after  counting  up  the  natural  number  to  a 
term  expressed  by  a  hundred  million  digits,  —  he 
writes :  "  If  every  letter  now  before  the  reader's  eye 
were  changed  into  a  figure,  and  if  all  the  figures  con- 
tained in  a  thousand  such  volumes  were  arranged 
in  order,  the  whole  together  would  yet  fall  far 
short  of  the  vast  induction  the  observer  would  have 
had  in  favor  of  the  truth  of  the  law  of  natural  num- 
bers ;  yet  shall  the  engine,  true  to  the  prediction  of 
its  director,  after  the  lapse  of  myriads  of  ages,  fulfil 
its  task  and  give  that  one,  the  first  and  only  excep- 
tion, to  that  time-sanctioned  law."  What  would 
have  been  the  chances  in  favor  of  the  perfect  contin- 
uity of  the  series  immediately  prior  to  this  break? 
Certainly,  we  may  add,  as  great  as  are  the  chances 
that  the  sun  will  rise  to-morrow. 

Now  this  same  machine,  as  Mr.  Babbage  also 
showed,  may  be  so  constructed  and  set  as  to  change 
its  law  after  an  appointed  number  of  terms,  and  then 


170         babbage's  calculating  engine. 

proceed  to  follow  a  new  law  as  invariably  as  before. 
Thus,  after  giving  the  natural  numbers  for  a  certain 
period,  it  might  suddenly  begin  to  give  square  or 
cube  numbers ;  and  it  is  possible  to  conceive  of  a 
machine  by  which  such  transitions  might  be  indefi- 
nitely repeated. 

If  such  things  are  possible  in  human  mechanism, 
why  not  in  the  scheme  of  nature?  That  in  the 
short  history  of  science  we  have  not  observed  such 
changes  is  no  proof  that  they  may  not  take  place. 
If  they  do  come  to  pass  we  should  expect  from  all 
analogies  that  they  would  come  with  extreme  slow- 
ness, according  to  our  measures  of  time,  and  without 
observation.  And  certainly  during  the  geological 
ages  changes  have  come  to  pass  for  which  we  can 
give  otherwise  no  clear  account. 

Of  course  such  considerations  as  Babbage  has 
so  eloquently  urged  are  no  arguments,  but  they  do 
help  the  imagination ;  and  this  is  a  question  in  which 
the  imagination  has  raised  all  the  difficulty,  and  is 
therefore  chiefly  to  be  addressed. 

We  have  tacitly  assumed  thus  far  that  the  laws  of 
nature  are  all  equally  definite  and  equally  exact;  but 
this  is  very  far  from  being  true.  In  most  cases,  at 
least,  the  phenomena  correlated  under  a  law  admit 
of  a  more  or  less  wide  variation ;  and  the  proposi- 
tion which  we  call  a  law  is  an  ideal  rather  than  an 
actual  relation, —  an  abstraction,  rather  than  an  entity. 
This  is  the  next  point  to  which  I  wish  to  ask  your 
attention ;  and  its  bearing  on  the  previous  consider- 
ations is  obvious.  For  if  it  shall  appear  that  the  laws 
of  nature  vary  with  different  relations,  and  are  not 


DEFINITE   LAWS.  \Ji 


the  hard  and  fast  rules  which  have  been  assumed; 
that  they  are  modes  of  thought,  and  not  modes  of 
action ;  then  all  that  has  been  said  in  regard  to  the 
independence  of  causation,  and  the  possibility  of 
interference,  will  be  seen  to  have  still  greater  force 
than  at  first  appeared. 

Very  few  of  the  recognized  laws  of  nature  are  ab- 
solutely definite ;  and  of  these  few,  with  the  exception 
possibly  of  the  law  of  gravitation,  the  invariability 
must  be  assumed ;  for  it  cannot  be  proved,  at  least 
absolutely.  In  the  present  state  of  knowledge  we 
should  class  as  among  these  definite  laws,  the  law  of 
conservation  of  mass,  the  law  of  conservation  of 
energy,  the  laws  of  motion,  and  the  law  of  gravita- 
tion. Now,  although  we  may  have  no  question  that 
all  these  laws  are  absolutely  fixed,  and  can  never  be 
expected  in  the  least  degree  to  alter  in  their  mani- 
festation, yet  there  is  not  one  of  them  which  is  sus- 
ceptible of  experimental  proof,  except,  to  a  limited 
extent,  the  law  of  gravitation. 

Take,  for  example,  the  first  law  of  motion,  the  law 
of  inertia,  as  it  is  also  called,  and  which  we  have 
before  more  than  once  enunciated.  We  cannot 
demonstrate  experimentally  that  a  body  will  con- 
tinue in  a  state  of  motion  until  acted  on  by  some 
external  force.  On  the  surface  of  the  earth,  even 
under  the  most  favorable  conditions,  all  motion  is 
soon  arrested  by  friction,  or  by  some  other  mode  of 
impact ;  and  the  most  we  can  do  is  to  show  that  in 
proportion  as  such  resistances  are  removed,  the 
longer  the  motion  continues,  —  a  form  of  inference 
which  has  been  called  "  the  principle  of  successive 


172  LAW   OF   INERTIA. 

approach,"  but  which  is  obviously  no  proof.  Could 
the  law  of  inertia  be  verified  experimentally,  perpet- 
ual motion  would  be  possible;  but  even  with  all 
our  experimental  skill  we  have  not  made  the  most 
distant  approach  to  such  a  condition. 

It  is  a  mistake  of  ignorance  to  infer  that  perpetual 
motion  means  unlimited  work;  and  yet  it  is  this  very 
erroneous  inference  which  alone  gives  a  popular  in- 
terest to  the  question.  Work  done  by  a  moving 
body  necessarily  involves  loss  of  motion;  and  the 
effects  of  friction  are  merely  examples  of  this  general 
principle.  Perpetual  motion  is  theoretically  possible, 
but  work  without  the  loss  of  motion,  or  the  expendi- 
ture of  energy  in  some  form,  is  inconceivable ;  and 
the  assumption  implies  a  confusion  of  mechanical 
conceptions.  It  is  unnecessary  for  our  purpose  to 
dwell  on  this  point,  and  we  allude  to  it  only  because 
it  serves  indirectly  to  illustrate  the  character  of  the 
law  under  consideration.  Nor  need  we  do  more  than 
refer  to  the  grand  displays  of  perpetual  motion  re- 
vealed to  us  by  astronomy,  which  seem  at  first  sight 
to  be  most  conspicuous  illustrations  of  the  principle. 
But  the  law  is  here  so  overlaid  and  obscured  that 
observations  on  the  motions  of  the  planets  cannot 
be  regarded  as  a  direct  proof  of  its  validity.  Indeed, 
originally  the  law  was  an  assumption  made  to  ex- 
plain these  very  motions,  and  is,  therefore,  an  induc- 
tion based  on  astronomical  facts,  not  a  deduction 
that  can  be  demonstrated  by  them. 

As  with  the  law  of  inertia  so  is  it  with  the  law  of 
conservation  of  mass.  We  cannot  demonstrate  that 
the  amount  of  material    in  nature   has  never  been 


CONSERVATION   OF  MASS.  173 


increased  by  the  smallest  amount.  All  we  can  do 
in  any  case  is  to  show  that  the  amount  of  material 
with  which  we  experiment  is  not  perceptibly  altered 
in  the  various  transformations  through  which  it 
passes,  —  assuming  of  course  that  the  amount  of  ma- 
terial, or  to  use  a  technical  term,  the  mass,  is  accu- 
rately measured  by  the  weight.  In  a  chemical 
process,  when  we  can  weigh  all  the  materials  con- 
cerned, we  find  that  within  the  unavoidable  experi- 
mental errors,  often  very  large,  the  sum  of  the 
weights  of  the  products  of  the  process  is  exactly 
equal  to  the  sum  of  the  weights  of  the  factors ;  and 
after  a  very  wide  experience  with  similar  results  we 
assume  that  the  two  sums  are  always  exactly  equal. 
Hence  we  represent  every  chemical  process  as  an 
equation,  writing  on  the  left  of  the  sign  of  equality 
the  several  symbols  which  represent  the  weights  of 
the  factors,  and  on  the  right  the  corresponding  sym- 
bols which  represent  the  weights  of  the  products. 
Obviously,  however,  we  can  never  demonstrate  the 
exactness  and  universality  of  the  law  which  our 
chemical  equations  assume.  The  constancy  of  the 
law  is  of  necessity  a  question  of  inference.  Still,  as 
in  the  case  of  inertia,  we  can  appeal  to  phenomena 
which  render  the  inference  in  the  highest  degree 
conclusive. 

There  are,  for  example,  a  very  large  number  of 
chemical  processes  which  it  is  possible  to  conduct 
in  an  hermetically  closed  vessel,  —  as  in  a  sealed  pre- 
serve jar;  so  that  by  weighing  the  vessel  before 
and  after  the  experiment,  it  can  be  shown  that  no 
change  of  weight  has  come  from  the  chemical  pro- 


174  CONSERVATION   OF   MASS. 

cess  which  has  taken  place  inside,  —  a  result  which 
we  should  confidently  expect,  since  nothing  could 
get  in  or  out  of  the  sealed  vessel. 

The  burning  of  charcoal  in  oxygen  gas,  under 
such  conditions  as  just  described,  furnishes  a  very 
striking  illustration  of  the  principle  under  discussion. 
When  a  lump  of  charcoal  burns,  a  solid  material, 
the  fuel,  is  converted  into  an  aeriform  substance, 
the  smoke ;  and  the  result  seems  at  first  sight  glar- 
ingly to  contradict  the  assumed  law;  but  when  we 
burn  the  coal  in  a  closed  jar  it  is  obvious  that  as 
there  has  been  no  change  of  weight,  there  can  have 
been  no  loss  of  material;  and  it  is  further  evident 
that  the  substance  of  the  coal  must  have  been  ab- 
sorbed by  the  oxygen  gas  to  form  the  aeriform 
product  we  call  smoke. 

We  can  now  pass  to  the  earth  as  a  whole ;  and  re- 
garding our  dwelling-place  as  a  globe  isolated  in  space 
from  which  no  material  escapes,  and  into  which  none 
enters, —  except  an  occasional  meteorite, — we  can  at 
once  recognize  relations  similar  to  those  of  a  sealed 
jar,  in  which  all  terrestrial  nature  appears  as  a  grand 
illustration  of  the  conservation  of  mass.  But  obvi- 
ously such  illustrations,  although  they  may  be  the 
basis  of  well-founded  inferences,  are  no  proofs  of  the 
absolute  exactness  and  invariability  of  the  law;  and 
a  study  of  either  of  the  other  laws  we  have  classed 
as  exact  would  bring  out  the  same  features.  But 
this  is  a  subsidiary  point,  and  it  is  not  necessary  to 
dwell  upon  it  further. 

The  laws  classed  as  exact  present  also  another 
character  worthy  of  your  consideration,  which,   al- 


FUNDAMENTAL   CONDITIONS.  1 75 

though  it  cannot  be  definitely  formulated  in  the 
present  state  of  our  knowledge,  is  probably  funda- 
mental ;  and  it  distinguishes  these  special  cases  from 
the  great  body  of  the  laws  of  nature  whose  relations 
we  shall  study  later.  Such  principles  as  the  laws  of 
motion,  and  the  laws  of  conservation,  whether  of 
mass  or  of  energy,  seem  to  be  fundamental  relations 
of  the  material  universe;  and  not  the  modes  of  ac- 
tion of  external  agencies.  They  are  like  the  essen- 
tial qualities  of  matter,  —  extension,  impenetrability, 
mobility,  —  and  not  like  the  accidental  qualities,  which 
may  be  regarded  as  superimposed  upon  matter  by 
the  action  of  some  mode  of  energy,  —  such  as  color, 
temperature,  or  magnetism.  Consequently  they  are 
simple  instead  of  complex  relations. 

Consider,  for  instance,  inertia,  which  is  often  classed 
as  a  quality  of  matter.  This  is  not  an  active  but 
wholly  a  passive  relation,  as  the  common  use  of  the 
word  "  inert "  indicates.  Matter  has  no  power  within 
itself  to  change  its  state  or  condition  in  any  way. 
Such  changes  in  all  cases  imply  an  external  agent, 
and  an  expenditure  of  energy,  which  is  to  be  distin- 
guished from  the  passive  mass  on  which  it  acts. 

It  has  been  said  that  the  original  atoms  contained 
the  potency  of  all  possible  being;  and  if  by  this  is 
meant  that  they  were  the  beginnings  of  things,  — 

u  .  .  .  rudis  indigestaque  moles, 
Nee  quicquam  nisi  pondus  iners,  congestaque  eadem 
Non  bene  junctarum  discordia  semina  rerum,  —  " 

the  proposition  is  harmless  enough,  if  we  accept  the 
general  theory  that  atoms  are  the  final  result  of  the 


I76  POTENTIALITY   OF  ATOMS. 

analysis  of  matter;  but  if  it  is  meant  that  the  atoms 
have  actual  creative  potency,  and  all  future  being 
involved  in  their  substance,  in  the  same  sense  that 
the  flower  is  infolded  in  the  bud,  then  it  is  a  suffi- 
cient answer  to  all  such  speculations  to  say  that 
they  are  wholly  at  variance1  with  the  manifest  ten- 
dency of  modern  science.  If  there  be  one  thing 
more  marked  in  that  tendency  than  another,  it  is  to 
distinguish  energy  and  matter  as  two  distinct  and 
separate  entities ;  and  to  regard  matter  as  wholly 
inert,  utterly  lifeless  and  dead,  except  in  so  far  as  it 
is  controlled  and  energized  from  without.  We  be- 
lieve this  to  be  the  correct  view,  not  only  in  regard 
to  such  manifestations  of  material  bodies  as  we  refer 
to  heat,  light,  and  electricity ;  but  also  in  regard  to 
those  seemingly  inherent  forces  which  hold  the  parts 
of  a  body  together,  and  determine  the  effects  of 
cohesion,  elasticity,  and  the  like. 

For  example,  we  distinguish  among  the  conditions 
of  magnetic  phenomena  what  we  call  the  "  field  of 
force."  Masses  of  iron  brought  into  that  field — that 
is,  into  any  space  thus  conditioned  —  become  at  once 
magnetic,  and  attract  or  repel  each  other  as  the  case 
may  be.  Now  it  is  a  plausible  conception  that  we 
live  in  a  space  conditioned  not  only  by  magnetism, 
but  by  various  other  agencies,  which  may  determine 
the  cohesion  and  structure  of  solid  bodies.  Every 
year  I  show  to  my  class  an  experiment  which  I 
never  witness  myself  without  being  strongly  im- 
pressed by  the  wonderful  relations  which  it  illus- 
trates, and  the  still  more  wonderful  relations  it 
suggests.     On    the   top   of  a   board,  resting   on   the 


FIELD   OF   FORCE.  177 


poles  of  a  powerful  electro-magnet,  I  place  a  large, 
loose  pile  of  wrought-iron  nails.  When  the  current 
of  a  dynamo-machine  passes  through  the  coil  of  the 
instrument,  a  magnetic  field  is  established  through- 
out all  the  space  in  the  neighborhood  of  the  poles ; 
and  with  this  the  board  in  no  way  interferes,  al- 
though it  keeps  the  nails  from  direct  contact  with 
the  magnet  itself.  As  soon  as  the  current  passes, 
and  the  field  is  established,  the  loose  nails,  by  their 
mutual  attractions,  —  thus  determined,  —  become  a 
tough,  plastic  mass,  which  can  be  moulded  into  the 
form  of  an  arch,  or  of  any  similar  structure.  But 
when  the  current  is  broken  the  magnetic  virtue  of 
the  field  disappears,  and  the  structure  that  had  been 
reared,  crumbles  into  nails.  Analogy  suggests  that 
the  atoms  of  matter,  inert  in  themselves,  are  simi- 
larly conditioned,  and  that  all  structures  would  be 
resolved,  and  all  forms  of  matter  disappear,  if  the 
Presence  which  sustains  them  were  withdrawn. 

Now,  just  as  the  first  law  of  motion  appears  to  be 
merely  a  declaration  of  a  passive  quality  of  matter, 
so  it  seems  to  me  all  the  other  laws  we  have  classed 
as  exact  are  fundamental  attributes  either  of  matter 
or  of  energy.  This  may  not  appear  as  the  laws  are 
usually  stated ;  but  an  analysis  of  the  relations  thus 
enunciated  will  always  show  their  true  character. 
Thus  in  regard  to  the  law  of  conservation  of  mass, 
to  which  we  have  just  referred  in  another  connection, 
—  it  would  be  easy  so  to  state  the  law  as  to  make  it 
appear  arbitrary  and  anomalous.  That  in  every 
chemical  change  the  sum  of  the  weights  of  the  prod- 
ucts formed  should  be  exactly  equal  to  the  weights 


178  CONSERVATION   OF   MASS. 

of  the  factors  consumed ;  for  example,  that  when 
water  is  resolved  by  an  electrical  current  into  oxygen 
and  hydrogen,  the  combined  weights  of  these  two 
aeriform  substances  should  be  exactly  equal  to  the 
weight  of  the  liquid  water  used  up  in  the  process ; 
or,  what  is  still  more  remarkable,  that  when  coal  or 
wood  burn,  the  weight  of  the  smoke  added  to  the 
weight  of  the  ashes  will  be,  to  the  smallest  fraction  of 
a  grain,  exactly  equal  to  the  weight  of  the  fuel  which 
has  disappeared,  and  for  the  most  part  flown  up  the 
chimney,  —  all  this  does  seem  at  first  sight  to  be  such 
a  precise  conformity  to  weights  and  measures  as 
could  never  have  been  secured  unless  specially  or- 
dained ;  but  a  few  moments'  consideration  will  show 
that  this  law,  so  far  from  being  an  ordinance  super- 
imposed as  it  were  upon  matter,  is  a  relation  neces- 
sarily arising  from  its  very  constitution.  In  any 
mechanical  process  you  at  once  recognize  that  there 
can  be  no  real  loss  of  material.  When  silver  and 
gold  bullion  are  coined  or  made  into  ware  and  trink- 
ets, you  confidently  expect,  from  your  knowledge  of 
material  relations,  to  find  all  the  metal  in  the  manu- 
factured articles,  —  of  course  excepting  a  small  loss 
from  dispersion  by  attrition,  abrasure,  or  otherwise, 
for  which  you  can  readily  account.  Why  should  not 
the  same  be  true  in  a  chemical  process?  If  there  be 
no  loss  of  precious  metal  when  one  hundred  pounds 
of  silver  are  coined  at  the  mint,  why  should  there  be 
any  loss  when  the  same  amount  of  bullion  is  con- 
verted into  nitrate  of  silver  by  the  manufacturing 
chemist?  Certainly,  not  only  can  we  find  no  "suffi- 
cient reason "   for  expecting  a  change   of  relations 


LAW   OF   COMBINING   PROPORTIONS.  1 79 

under  such  circumstances,  but  also  the  more  we 
study  material  relations  the  more  evident  does  it 
appear  that  conservation  of  mass  is  simply  the  mani- 
festation of  the  persistency  of  the  mode  of  being  we 
call  matter.  In  other  words,  the  study  of  the  rela- 
tions of  matter,  and  even  our  own  familiar  experience, 
has  produced  the  conviction  that  beneath  the  eva- 
nescent qualities  of  changing  substances  and  the  de- 
caying forms  of  organic  structures,  there  is  a  material 
substratum  which  is  permanent  and  unchangeable; 
and  that  the  law  of  chemistry  we  have  been  studying 
is  simply  the  manifestation  of  this  fundamental  es- 
sence of  matter.  The  illusion  which  is  produced  by 
the  escape  of  colorless  aeriform  matter  in  the  burning 
of  fuel,  and  in  many  other  less  familiar  chemical  pro- 
cesses, is  easily  corrected  by  conducting  the  ex- 
periment in  an  air-tight  vessel,  as  we  have  before 
described. 

The  same  essential  feature  appears  in  the  second 
of  the  great  laws  of  chemistry,  which  we  have  already 
described  as  the  law  of  combining  proportions. 
That  hydrogen  gas  should  combine  with  oxygen  gas 
to  form  water  in  the  exact  proportions  of  2.000  to 
15.869,  as  was  shown  in  the  last  lecture,  does  seem 
at  first  sight  as  accidental  or  arbitrary  a  relation  as 
could  well  be  imposed  on  these  elementary  sub- 
stances ;  but  if  we  look  at  the  subject  from  another 
point  of  view,  it  will  be  seen  that  some  definiteness  of 
relation  is  implied  by  the  other  essential  attributes  of 
matter,  even  though  our  present  knowledge  may  not 
enable  us  to  see  the  reason  of  the  precise  value  of 
the  proportion  in  a  given  case.     It  is  obvious,  for 


ISO  LAW   OF   COMBINING   PROPORTIONS. 

example,  that  assuming  the  supply  of  oxygen  unlim- 
ited, we  should  expect  to  obtain  twice  as  much  water 
by  burning  twice  as  much  hydrogen ;  and  so,  on  the 
other  hand,  were  the  supply  of  hydrogen  unlimited, 
we  should  expect  the  same  result  by  using  twice  as 
much  oxygen ;  otherwise  all  our  knowledge  of  ma- 
terial relations  would  be  confounded.  But  this  implies 
that  the  relative  weights  of  hydrogen,  oxygen,  and 
water,  which  concur  in  the  familiar  process  of  burning 
hydrogen  gas,  must  be  definite,  —  although  we  have 
no  means  of  predicting  that  the  definite  proportion 
should  be  exactly  that  of  2.000  to  15.869  to  17.869. 

Take,  as  another  example,  the  simple  chemical  pro- 
cess which  results  when,  we  bring  together  carbonate 
of  soda,  hydrochloric  acid,  and  water.  The  products 
of  this  process  are  common  salt,  carbonic  acid  gas, 
and  a  small  additional  amount  of  water.  Here  again 
common-sense,  as  we  might  say,  tells  us  that  we  must 
proportion  our  carbonate  of  soda  to  the  amount  of 
carbonic  acid  gas  we  desire  to  make.  If  we  need 
three  times  as  much  gas  we  must  take  three  times  as 
much  soda,  and  so  in  regard  to  any  of  the  other 
materials  concerned  in  the  process ;  but  this  implies 
a  definite  relation  between  the  several  factors  and 
products  of  the  chemical  change,  or,  in  other  words, 
this  familiar  experience  and  common-sense  imply 
the  law  of  definite  proportions. 

In  the  two  cases  last  cited  these  so-called  laws  of 
chemistry  are  evidently,  as  we  have  before  said, 
merely  fundamental  relations  of  matter,  and  not  the 
modes  of  action  of  external  agents.  To  the  same 
category  belongs  the  law  of  conservation  of  energy, 


LAW   OF  GRAVITATION.  l8l 

and  so  obviously  that  I  need  not  press  the  point ;  but 
in  regard  to  the  great  law  of  gravitation  there  is  a 
manifest  difficulty  of  interpreting  the  phenomena 
from  this  point  of  view.  As  we  have  already  pointed 
out,  the  usual  statement  of  the  law  implies  an 
attractive  force,  and  therefore  an  active  power  of 
great  potency.  Nevertheless,  I  am  inclined  to  the 
opinion  that  here  also  the  facts  are  best  explained 
on  the  view  that  gravitation  is  simply  a  manifesta- 
tion of  a  fundamental  relation  between  energy  and 
mass. 

There  are  several  circumstances  which  would  sup- 
port the  opinion  thus  expressed,  although  I  have 
only  time  to  allude  to  them  here.  In  the  first  place, 
gravity  is  the  only  attractive  force  which  is  directly 
proportional  to  the  mass.  Magnetic  and  electrical 
attractions  follow  wholly  different  and  far  more  com- 
plex laws.  In  the  second  place,  the  diminution  of 
gravity  with  the  square  of  the  distance  is  simply  the 
law  of  the  diffusion  of  any  radiant  energy  through 
space;  as  may  be  seen  in  the  intensity  of  illumination 
on  screens  at  different  distances  from  a  luminous 
source.  In  the  third  place,  the  attraction  of  one 
mass  is  not  in  the  least  influenced  by  the  proximity 
of  similarly  attracting  masses.  Thus,  each  of  two 
weights  on  a  scale-pan  exerts  its  specific  effect  inde- 
pendent of  its  association ;  but  two  magnets  or  two 
electrified  bodies  when  placed  in  juxtaposition  do 
not  exert  the  same  invariable  concurrent  action.  In 
the  fourth  place,  the  attraction  of  gravity  is  wholly 
independent  of  the  intervening  medium.  Two  bodies 
on  the  opposites  sides  of  this  globe  would  attract 


1 82  LAW   OF   GRAVITATION. 

each  other  with  the  same  force  whether  the  earth 
were  in  the  way  or  not;  while  electrical  or  magnetic 
attraction  is  very  greatly  influenced  by  the  nature  of 
the  dielectric  or  diamagnetic  which  intervenes.  In 
fine,  activities  which  are  superinduced,  like  electrical 
or  magnetic  attractions,  follow  wholly  different  and 
vastly  more  complex  laws  than  the  simple  relations 
to  mass  and  space  which  gravity  exhibits.  Hence 
the  grounds  of  the  opinion  expressed  above  that  the 
law  of  gravitation  is  a  proposition  which  expresses, 
not  the  mode  of  action  of  a  special  force  or  agency, 
but  simply  a  fundamental  and  necessary  relation 
between  energy  and  mass. 

I  freely  admit  that  the  opinion  I  have  expressed 
in  regard  to  the  laws  classed  as  exact  may  be  open 
to  philosophical  objections,  and  I  do  not  advance  it 
as  a  well-grounded,  much  less  as  an  accepted  doc- 
trine. Since,  however,  I  expect  to  show  in  my  next 
lecture  that  the  great  body  of  natural  laws,  as  enun- 
ciated in  our  systems  of  science,  are  merely  ideal 
relations,  which  the  phenomena  of  nature  approach, 
but  which  are  rarely  if  ever  realized,  I  felt  it  incum- 
bent on  me  to  give  a  clear  account  of  those  funda- 
mental principles  that  appear  to  be  more  exact. 
My  one.  object  is  to  make  clear  to  you  the  aspect 
of  the  laws  of  nature  as  seen  from  the  standpoint 
of  a  student  of  physical  science,  with  all  the  in- 
definiteness  which  the  view  presents,  and  with  the 
impenetrable  clouds  which  limit  the  prospect  on 
every  side.  Do  not,  however,  accept  my  opinions, 
or  rely  on  my  judgment;  but  study  the  phenomena 
for  yourselves,  not  as  drawn  in  sharp  outlines  by  popu- 


CAUTION   REQUIRED.  183 

lar  writers,  but  as  exhibited  by  nature,  with  all  their 
limitations,  all  their  variations,  and  all  their  obscurity. 
Make  sure  of  the  actual  facts;  so  that  you  shall  build 
your  philosophy  on  a  firm  and  enduring  basis  that 
cannot  be  moved. 


13 


1 84  LAW   OF   MARIOTTE. 


LECTURE   VII. 

DETERMINATE  AND  INDETERMINATE  LAWS. 

OF  the  great  body  of  the  laws  of  physical  science 
which  are  described  in  the  treatises  on  physics 
or  chemistry,  I  could  not  select  a  fairer  illustration 
than  the  law  of  Mariotte.  This  law  was  discovered 
during  the  last  half  of  the  seventeenth  century,  wholly 
independently,  by  the  Abbe  Mariotte  in  France  and 
by  the  famous  English  philosopher  Boyle,  and  is 
often  called  by  English  writers  "  the  law  of  Boyle." 
Since  that  time  all  the  relations  of  the  law  have  been 
repeatedly  and  carefully  investigated,  and  there  are 
few  principles  of  science  in  regard  to  which  our 
knowledge  is  more  precise.  According  to  the  usual 
formula  this  law  declares  that  the  volume  of  a  given 
mass  of  gas  is  inversely  as  the  pressure  to  which  it 
is  exposed ;  or  in  other  words,  that  as  the  pressure 
increases  or  diminishes,  the  volume  contracts  or  ex- 
pands in  precisely  the  same  proportion.  For  exam- 
ple, if  we  have  a  perfectly  flexible  balloon,  partially 
inflated,  the  volume  of  the  confined  gas  will  contract 
or  expand  in  absolutely  the  same  proportion  as  the 
pressure  of  the  air  on  the  outside  is  increased  or 
diminished.    We  can  also  enunciate  the  law  in  another 


CONCOMITANT   CONDITIONS.  1 85 

form,  which  applies  to  any  mass  of  aeriform  matter, 
whether  confined  or  not,  —  saying  that  the  density  of 
a  given  atmosphere  is  directly  proportional  to  its 
tension.  But  since  the  tension  of  a  gas  must  neces- 
sarily balance  the  pressure  to  which  it  is  exposed, 
and  since  the  density  of  a  gas  must  increase  as  its 
volume  diminishes,  the  last  statement  only  describes 
another  phase  of  the  same  principle. 

This  law  discovered  by  Mariotte  is  of  fundamental 
importance  in  many  departments  of  chemistry  and 
physics,  especially  in  meteorology;  but  in  nature  its 
simple  working  rarely  if  ever  appears.  The  volume 
and  density  of  a  mass  of  aeriform  matter  not  only 
varies  with  the  external  pressure  or  internal  tension, 
but  similar  and  as  great  changes  are  caused  by  varia- 
tions of  temperature.  Considerable  although  less 
marked  effects  are  produced  by  moisture,  and  in  pass- 
ing from  one  place  to  another  a  sensible  change  may 
be  caused  by  the  variations  in  the  intensity  of  gravity. 
In  any  case  the  observed  phenomenon  is  the  resultant 
of  all  these  partial  effects,  which  may  either  concur  or 
tend  to  balance  each  other.  Constantly,  then,  in 
practice,  the  law  must  be  disguised  and  its  action 
obscured.  The  same  is  true  of  all  similar  laws.  The 
phenomena  of  nature  are  usually  very  complex  results, 
and  such  laws  as  the  one  we  are  discussing  are  the 
simpler  elements  into  which  we  attempt  to  analyze 
the  phenomena.  But  this,  although  a  perplexing,  is 
only  an  incidental  circumstance,  and  we  must  con- 
sider the  aberrations  of  the  law  itself. 

Even  when  abstracted  from  all  concomitant  condi- 
tions, so  far  is  the  law  of  Mariotte  from  exact  that  it 


1 86  DEVIATIONS   FROM   THE   LAW. 

holds  absolutely  in  no  single  instance,  unless  inferen- 
tially  as  a  passing  phase  of  a  continuous  change. 
When  we  study  the  subject  minutely  and  pay  regard 
to  small  differences  we  find  that  each  distinct  aeriform 
substance  has  a  rate  of  its  own,  and  is,  as  it  were,  a 
law  unto  itself.  At  the  common  temperature  most 
gases,  as  nitrous  oxide,  carbonic  acid,  ammonia, 
oxygen,  nitrogen,  and  the  mixture  of  the  last  two  we 
call  air,  contract  under  pressure  to  a  perceptibly 
greater  extent  than  the  law  authorizes.  At  high 
pressures  the  deviation  becomes  very  marked,  and  as 
we  approach  the  pressures  under  which  the  gases 
are  condensed  to  liquids  no  semblance  of  the  law  is 
left.  Hydrogen,  on  the  other  hand,  the  lightest  con- 
dition of  aeriform  matter,  alone  contracts  less  than  the 
law  requires.  Hydrogen  therefore  seems  to  present 
unique  relations,  and  to  stand  apart  by  itself.  But 
the  experiments  of  Regnault  indicate  that  this  rela- 
tion depends  to  a  large  extent  on  temperature.  He 
observed  that  although  carbonic  acid  deviates  widely 
from  the  law  of  Mariotte  at  the  freezing-point  of 
water,  it  conforms  almost  precisely  to  it  at  the  boiling- 
point.  So  also  he  noticed  that  air  deviates  from  the 
law  much  less  at  an  elevated  temperature  than  at  the 
ordinary  temperature  of  the  atmosphere  ;  and  he  con- 
cluded that  a  temperature  could  easily  be  attained  at 
which  the  deviation  would  become  insensible  to  our 
means  of  observation.  He  even  thought  it  probable 
that  at  a  very  high  temperature  the  air  would  again 
deviate  from  the  law,  but  in  the  opposite  direction,  like 
hydrogen  at  the  ordinary  temperature.  Generalizing 
these  observations  it  is  supposed  that  the  same  would 


HISTORY   OF  THE   LAW.  1 87 

be  true  of  all  gases,  —  namely,  that  with  each  aeriform 
substance  there  is  some  temperature  at  which  it  con- 
forms to  Mariotte's  law ;  that  at  all  temperatures  below 
this  point  the  gas  is  compressed  more  than  the  law 
authorizes,  and  at  all  temperatures  above  this  point  it 
is  compressed  less  than  the  law  demands.  In  a  word, 
the  law  is  an  ideal  relation,  which  is  realized,  if  at  all, 
only  under  the  concurrence  of  conditions  which  it  is 
impossible  to  command. 

Mariotte's  law  illustrates  in  a  very  forcible  manner 
the  character  of  the  large  class  of  the  so-called  laws 
of  nature  we  are  considering,  and  its  history  furnishes 
one  of  the  best  examples  of  refined  scientific  investi- 
gation. I  could  readily  multiply  examples,  but  further 
discussion  would  be  tedious,  and  would  add  nothing 
to  the  force  of  my  argument;  for  I  feel  confident 
that  it  will  be  generally  allowed  that  I  have  selected 
as  fair  and  as  typical  an  illustration  as  I  could  find. 
In  my  work  on  "  Chemical  Physics  "  I  have  given  at 
some  length  the  history  of  the  law  of  Mariotte,  and  I 
would  refer  you  to  that  book  for  the  details ;  feeling 
confident  that  while  they  fully  bear  out  the  impres- 
sion I  have  endeavored  to  give  here  in  a  few  words, 
a  careful  study  of  the  particulars  will  give  you  a  much 
larger  comprehension  of  the  subject  I  am  seeking  to 
illustrate.  In  bare  outline  the  history  can  be  briefly 
told. 

The  compressibility  of  gases  was  in  the  first  place 
studied  with  a  comparatively  rude  apparatus,  and  a 
simple  law  was  discovered,  which  was  accepted  as 
the  absolute  truth.  Later,  when  the  methods  of 
investigation    had    become    more   accurate,    it    was 


1 83  THE   GRAPHICAL   METHOD 

found  that  the  law  was  not  general;  but  it  was  still 
maintained  in  regard  to  air,  until  finally  the  refined 
experiments  of  Regnault  proved  that  it  failed  here 
also.  Still  the  law  remains  as  an  ideal  truth  toward 
which  nature  tends,  but  which  is  never  fully  reached, 
and  we  can  even  trace  the  action  of  the  agents  which 
produce  the  perturbations.  So  it  is  with  most  physi- 
cal laws.  They  are  not  realized  with  mathematical 
exactness,  but  are  ideal  truths  always  more  or  less 
false  in  each  particular  case.  When  we  are  able  to 
go  behind  the  phenomena  to  their  proximate  causes, 
we  shall  undoubtedly  find  that  the  law  and  its  varia- 
tions are  merely  different  phases  of  the  workings  of 
one  complex  system ;  but  it  is  doubtful  whether  by 
man's  limited  powers  the  anomalies  of  nature  will 
ever  be  fully  explained,  or  its  discords  resolved. 
More  probably,  as  we  go  forward  in  our  investiga- 
tions, and  continually  widen  our  generalizations,  the 
last  generalization  of  all  will  bring  us  into  the  pres- 
ence of  that  Intelligence  of  which  all  natural  phe- 
nomena are  the  direct  manifestation. 

When  a  physicist  can  discover  no  simple  relations 
between  conditions  or  phenomena  obviously  inter- 
dependent, his  usual  method  of  proceeding  is  to  plot 
his  observations  on  paper,  on  some  system  of  co- 
ordinates, and  draw  a  curve  through  the  points  thus 
found.  The  process  is  a  simple  one,  and  with  the 
aid  of  an  example  can  easily  be  made  intelligible, 
even  to  those  who  do  not  understand  the  technical 
terms  with  which  the  so-called  graphical  method  is 
usually  described. 

The  solubility  of  a  substance  in  water  varies  with 


OF   REPRESENTING   PHYSICAL   RELATIONS.       1 89 

the  temperature,  usually  increasing,  but  sometimes 
diminishing,  as  the  temperature  rises,  and  at  rates 
which  vary  with  different  substances  between  wide 
limits.  There  is  an  obvious  connection  between  the 
weight  of  a  substance  which  will  dissolve  in  one 
hundred  parts  of  water  and  the  temperature ;  but 
no  definite  law  connecting  these  quantities  can  be 
discovered.  Assume  that  we  have  determined  ex- 
perimentally the  weight  in  grams  of  some  salt,  for 
example,  nitre  (KNOs),  that  will  dissolve  in  one 
hundred  grams  of  water  at  various  temperatures  be- 
tween its  freezing  and  boiling  points,  and  that  we 
have  tabulated  the  results.  Assume  also  that  we  have 
a  sheet  of  what  is  called  "  co-ordinate"  paper,  divided 
off  into  little  squares  like  a  multiplication  table,  as 
in  the  accompanying  figure.  On  the  lower  horizon- 
tal line,  called  the  "  axis  of  abscissas,"  we  mark  off 
the  temperature  in  degrees,  and  on  the  left-hand  ver- 
tical line,  called  the  "axis  of  ordinates,"  we  mark  the 
weight  in  grams.  Taking  now  the  data  we  have  tab- 
ulated, and  noticing  that  at  o°  thirteen  grams  of  nitre 
(KNO3)  dissolve  in  one  hundred  parts  of  water,  we 
follow  up  the  vertical  line  marked  o°,  until  we  come 
to  the  horizontal  line  marked  thirteen  grams,  and 
there  fix  the  first  point.  Seeing  next  that  at  150 
one  hundred  grams  of  water  dissolve  twenty-five 
grams  of  nitre,  we  follow  up  the  vertical  line  marked 
1 50  to  the  horizontal  line  marked  twenty-five  grams, 
and  the  intersection  fixes  a  second  point.  As  at 
300  one  hundred  grams  of  water  dissolve  forty-five 
grams  of  nitre,  we  find  a  third  point  by  following  up 
the  vertical  line  marked  300  to   the    horizontal  line 


190 


THE   GRAPHICAL   METHOD 


marked  forty-five  grams  ;  and  so  we  proceed  with 
each  of  the  experimental  data  we  have  found.  Thus 
we  obtain  as  many  points  as  there  are  observations, 
and  then  with  a  free  hand  we  draw  a  curve  as  nearly 
as  possible  through  all  the  points.  On  the  diagram 
we  have  given,  a  number  of  curves  showing  the  vary- 
ing solubility  of  several  chemical  compounds  in  water 
have  been   thus   drawn.      Such  curves   represent  to 


the  eye  what  has  been  called  the  "  law  of  the  vari- 
ation," using  however  the  word  "  law  "  in  a  still  less 
definite  sense  than  we  have  as  yet  employed  it. 
They  not  only  exhibit  the  general  order  of  the  phe- 
nomena, but  they  enable  us  to  fix  with  close  approx- 
imation values  between  the  points  at  which  the 
observations  were  made.  Thus  we  see  from  the 
figure  above  that  while  the  solubility  both  of  potas- 
sium chloride  (K  CI)  and  of  barium  chloride  (Ba  Cl2) 


OF   REPRESENTING    PHYSICAL   RELATIONS.      191 

increases  slowly,  but  at  a  uniform  rate  with  the  tem- 
perature, the  solubility  of  nitre  (K  N  Os)  varies  very 
rapidly,  and  at  a  constantly  increasing  rate.  Again, 
the  solubility  of  sodium  sulphate  (Na2  S04)  presents 
what  is  called  a  singular  point,  increasing  rapidly 
up  to  340  and  then  diminishing.  Lastly,  if  we  wish 
to  determine  the  solubility  at  a  given  temperature 
of  any  of  the  salts  here  represented,  we  have  only 
to  follow  up  the  vertical  line  corresponding  to  the 
temperature,  until  it  intersects  the  curve  of  the 
substance  in  question.  Then  on  following  from 
the  point  of  intersection  the  horizontal  line  to  the 
left,  we  read  off  on  the  vertical  axis,  the  number 
of  grams  of  the  substance  which  will  dissolve  in 
one  hundred  parts  of  water  at  that  temperature. 
Other  physical  phenomena  can  be  plotted  and  in- 
terpreted in  a  similar  way. 

Every  algebraic  equation  involving  two  variable 
quantities  corresponds  to  some  kind  of  plane  curve; 
and  so,  on  the  other  hand,  every  plane  curve  may  be 
represented  symbolically  by  an  algebraic  equation 
of  a  more  or  less  complex  character,  containing  the 
unknown  quantities.  Thus,  for  example,  the  solu- 
bility of  nitre  graphically  represented  by  the  curve 
above  described,  may  also  be  expressed  by  the 
equation  — 

S  =  13.32-}- 0.5738/ -(-o.oi7i6S/2-[-o.ooooo35977/3 

in  which  t  stands  for  the  temperature  in  degrees 
centigrade,  and  S  for  the  number  of  grams  of  salt 
which  at  this  temperature  will  dissolve  in  one  hun- 
dred  grams  of  water.     In  this  expression  the  value 


192  ALGEBRAIC   EXPRESSION. 

of  one  of  the  variables,  the  quantity  sought,  is  given 
in  the  terms  of  the  ascending  powers  of  the  other 
variable,   in  this  case  the  temperature,  —  each  term 
being   multiplied    by  a  numerical  coefficient,  whose 
values  are  deduced  from  experimental  data.     Equa- 
tions of  this  general  form  are  the  simplest,  although 
not  always  the  most  concise,  means  by  which  such 
relations    can  be    algebraically  expressed.     The  sci- 
ence of  mathematics,  however,  gives  us  the  means  of 
treating  the  subject  exhaustively,  so  that  after  distrib- 
uting the  errors,  we  can  express  our  results  in  the 
most  concise  manner  of  which  the  observations  admit, 
as  well  as  in  the  form  best  adapted  to  computation. 
It  furnishes  us  with  methods  and  guides  for  interpola- 
ting,  —  that  is,  of  calculating  from  numerical  results  of 
definite  experiments,  what  would  have  been  the  value 
of  intermediate  results,  —  or  even  for  assigning  values 
beyond  the  limits  of  the  experimental  data,  exterpo- 
lating,  as  Airy  called  it.     But  in  its  details  this  sub- 
ject cannot  be  understood  without  some  knowledge 
of  mathematics ;   and  further  discussion  would  be  out 
of  place  in  these  lectures.     It  is  only  with  the  broader 
relations  of  the  subject  that  we  are  here  concerned ; 
and  it  is  obvious  that  such  algebraic  expressions  as 
I  have  described  represent  what  we  may  call  an  in- 
determinate   law.     Such   expressions   are  sometimes 
called  empirical  laws,  because  they  are  really  conven- 
tional expressions  of  the  results  of  experiments,  and 
can  never  be  trusted  far  beyond  the  limits  of  the  ex- 
perimental data.     From  another  point  of  view  these 
formulae  may  be  regarded  simply  as  methods  of  ap- 
proximation to  indeterminate  results. 


THREE   CLASSES   OF   LAWS.  1 93 

Still,  in  discussing  the  nature  and  character  of  the 
laws  of  nature,  these  important  modes  of  representing 
physical  relations  must  not  be  overlooked,  and  they 
may  be  regarded  as  a  third  class  of  laws ;  so  that  we 
have  to  distinguish  the  fixed  laws,  like  the  laws  of 
motion,  the  determinate  laws,  like  the  law  of  Mariotte, 
and  the  indeterminate  laws,  such  as  we  have  just  de- 
scribed. That  these  last  are  in  the  fullest  sense  mere 
abstractions  is  sufficiently  evident  from  what  has 
already  been  said ;  but  after  all,  they  do  not  differ 
essentially  from  the  more  determinate  laws,  as  will 
appear  from  this  final  consideration. 

In  those  laws  which  can  only  be  geometrically  or 
algebraically  expressed,  we  find  the  greatest  differ- 
ences in  the  complexity  of  the  relations  which  the 
curves  or  formulae  exhibit;  and  sometimes  the  ex- 
pression is  so  simple  that  it  might  well  be  questioned 
under  which  of  the  two  artificial  categories  we  have 
made,  the  given  relation  should  be  classed.  Between 
classes  which  thus  blend  there  are  not  usually  any 
essential  differences,  and  such  differences  as  we  find 
probably  depend  on  the  greater  or  less  complexity 
of  the  phenomena  under  consideration.  The  distinc- 
tion between  the  fixed  and  the  variable  laws  appears 
to  be  more  fundamental;  and  the  first,  as  we  have 
before  said,  seem  to  be  expressions  of  the  essential 
properties  or  relations  of  matter  and  energy. 

The  conception  of  the  distinction  I  have  drawn  as 
it  exists  in  my  own  mind,  may  be  readily  illustrated 
by  the  well-known  Jacquard  loom,  which  with  numer- 
ous modifications  is  used  for  weaving  almost  every 
kind  of  fabric  having  inwrought  designs.     In  such  a 


194  JACQUARD   LOOM. 


machine,  a  carpet-loom  for  example,  although  the 
parts  work  in  harmony,  we  may  distinguish  between 
the  essential  machinery  of  a  loom  common  to  all 
looms,  and  the  ingenious  devices  of  Jacquard  by  which 
the  pattern  is  determined.  Without  these  additions, 
the  loom  would  weave  a  perfectly  uniform  plain 
fabric,  with  fixed  and  unvarying  relations  of  the  woof 
and  warp  ;  but  Jacquard's  perforated  cards  determine 
a  selection  of  the  threads,  and  through  a  combination 
of  these  variable  conditions,  so  complex  that  the  ob- 
server cannot  follow  their  intricate  workings,  the  pre- 
designed pattern  appears. 

So  is  it,  as  it  seems  to  me,  in  the  loom  of  nature. 
Mass  and  energy  are  the  woof  and  warp,  with  their 
commingled  tints,  out  of  which  the  tissue  of  events 
has  been  woven ;  and  these  fundamental  relations  are 
fixed  and  invariable.  But  ten  thousand  changing 
conditions,  fore-ordained  by  Omniscience  and  di- 
rected by  Unerring  Wisdom,  select  the  threads,  and 
thus  gradually  the  great  design  is  unrolled. 

I  might  push  the  analogy  further;  but  such  simil- 
itudes are  of  value  only  as  suggestions  to  thought, 
and  I  leave  the  subject  to  your  reflections. 

From  the  very  necessities  of  the  case  the  analysis 
of  the  laws  of  nature,  which  I  have  given  in  this  lec- 
ture, is  far  from  complete ;  and  I  cannot,  therefore, 
hope  that  it  is  conclusive.  Only  in  proportion  as 
one  sees  clearly  is  it  possible  to  describe  clearly  what 
appears;  and  when  peering  through  a  mist  all  out- 
lines are  ill-defined.  But  such  is  the  condition  under 
which  the  investigator  must  work,  and  he  can  only 
tell  you  faithfully  what  he  thinks  he  discerns.     Some- 


EDUCATIONAL   ASPECTS.  195 

times,  however,  the  clouds  break,  and  he  gains  a 
vision  of  the  truth  in  its  glory;  and  I  trust  one  con- 
clusion at  least  remains  clear  to  you  after  this  dis- 
cussion. 

From  no  point  of  view  can  the  laws  of  nature  be 
regarded  as  efficient  causes ;  and  this  ruler  which  a 
materialistic  philosophy  has  attempted  to  enthrone 
over  the  universe  is  no  potentate  in  any  sense,  but 
merely  a  very  intangible,  indistinct,  and  protean 
mental  image  of  man's  abstraction. 

As  has  already  been  intimated,  this  sophistry  of 
materialism  has  been  very  widely  disseminated  in 
consequence  of  our  imperfect  methods  of  education. 
The  only  knowledge  of  material  relations  which  most 
even  of  our  educated  people  acquire  is  derived  from 
elementary  text-books,  whose  formal  statements  con- 
stantly convey  false  impressions ;  and  hence  arises 
much  of  the  fallacy  which  prevails.  It  may  not 
therefore  be  out  of  place  to  devote  the  remainder  of 
the  hour  to  a  short  discussion  of  the  educational 
aspects  of  our  subject. 

One  of  the  most  brilliant  and  influential  writers  of 
our  day,  while  fully  conceding  the  very  great  im- 
portance to  the  scholar  of  the  general  results  of 
science,  as  furnishing  an  essential  part  of  the  ma- 
terials of  modern  literature,  has  expressed  the  opinion 
that  the  details  and  methods  of  science  are  of  value 
chiefly  to  experts,  and  are  unfit  materials  to  form  the 
basis  of  liberal  culture. 

With  the  general  spirit  of  Mr.  Matthew  Arnold's 
address  on  "  Literature  and  Science  "  (first  delivered 
as  the  Rede  Lecture  at  the  University  of  Cambridge 


196  LITERATURE  AND   SCIENCE. 

in  England,  and  afterwards  often  repeated  in  this 
country)  I  entirely  sympathize.  I  freely  admit  that 
as  a  means  of  liberal  culture  that  knowledge  is  most 
important  which,  to  use  Mr.  Arnold's  striking  ex- 
pression, can  be  most  directly  related  to  the  sense 
for  beauty  and  the  sense  for  conduct;  as  well  as  I 
should  add  to  all  the  senses  which  make  up  that  won- 
derful composite  we  call  character.  Character  is  the 
great  end  of  education ;  and  that  which  arouses  in 
man  elevated  thoughts  and  conceptions,  and  that 
which  stirs  within  him  great  resolves  that  lead  to 
noble  deeds,  has  more  influence  on  character  than 
any  special  knowledge  however  profound,  and  how- 
ever valuable  in  itself  considered  to  the  welfare  of 
society. 

The  term  "  science  "  was  used  by  Mr.  Arnold  in  its 
broadest  sense,  to  include  any  body  of  systematized 
facts,  whether  of  nature  or  of  any  department  of 
human  learning;  and  I  wholly  agree  with  him  that 
the  mere  acquisition  of  knowledge,  however  useful,  is 
a  very  insufficient  means  of  liberal  culture ;  and  also 
that  it  is  equally  unimportant  to  the  great  mass  of 
educated  men  whether  the  products  of  the  combus- 
tion of  a  wax  taper  be  carbonic  acid  and  water,  or 
whether  the  genitive  plural  o>{  pais  and  pas  take  the 
circumflex  on  the  termination.  The  practice  in  so 
many  of  our  schools  of  cramming  immature  minds 
with  heterogeneous  information,  which  they  at  least 
are  unable  to  relate  to  the  sense  of  beauty,  to  the 
sense  of  conduct,  or  to  the  sense  of  fitness  of  any 
kind,  is  to  my  mind  a  waste  of  golden  opportunities, 
and  productive  of  no  permanent  good. 


CLAIMS   OF   SCIENCE.  1 97 

But  while  conceding  all  this,  I  claim  for  the  study 
of  physical  science,  if  rightly  pursued,  the  highest 
value,  even  when  judged  by  the  very  criteria  which 
Mr.  Arnold  has  so  acutely  laid  down.  The  grand  re- 
sults of  physical  science  are  most  closely  related  to 
the  sense  for  beauty,  and  to  the  sense  for  conduct; 
and  as  a  matter  of  fact  they  have  satisfied  the  needs 
of  the  noblest  men  for  beauty,  for  conduct,  —  and  for 
holiness  also,  —  as  fully  as  any  earth-born  knowledge 
ever  can.  The  beauty  of  God's  creation  loses  none 
of  its  loveliness  to  him  who  knows  the  fitness  of  all 
the  parts.  Beauty,  as  we  have  before  said,  is  simply 
that  harmony  of  proportions  and  qualities  which  re- 
sults from  the  most  complete  fitness  of  all  the  parts 
in  a  perfect  whole,  and  becomes  the  more  apparent, 
and  the  more  commanding,  in  the  exact  proportion 
as  that  fitness  becomes  known  and  appreciated 
through  study  and  investigation.  His  mind  must 
be  dull  indeed  whose  noblest  impulses  are  not  awak- 
ened, and  aroused  to  action,  by  the  revelations  of  in- 
telligence and  forethought  which  come  from  the 
study  of  the  material  universe;  and  we  can  aptly 
quote,  though  with  a  somewhat  different  interpreta- 
tion, the  refrain  of  Mr.  Arnold's  noble  address,  — 
"  no  wisdom,  nor  understanding,  nor  counsel,  against 
the  eternal !  " 

Passing  now  for  a  moment  from  the  subject  matter 
to  the  methods  of  science,  I  may  venture  to  assert,  as 
the  conclusion  from  an  unusually  long  experience  as 
a  teacher,  that  no  one  can  acquire  an  adequate 
knowledge  of  scientific  results  without  such  an  ac- 
quaintance  with   the   methods  by  which  the  results 


198         KNOWLEDGE   OF  METHODS   ESSENTIAL. 

were  obtained  as  will  give  a  correct  appreciation  of 
the  limitations  under  which  the  conclusions  must  be 
received ;  and  that  in  many  cases  no  language,  how- 
ever skilfully  used,  is  adequate  to  convey  an  accurate 
conception  of  the  truth.  A  student  must  observe 
and  experiment  for  himself  if  he  would  acquire  clear 
and  correct  ideas  of  natural  phenomena.  Every 
teacher  of  experience  knows  that  the  conceptions 
acquired  from  elementary  text-books  and  popular 
lectures  are  constantly  erroneous,  and  often  absurd. 

Take  such  a  simple  result  of  chemistry  as  that 
water  is  composed  of  oxygen  and  hydrogen.  I  am 
sure  from  my  own  experience  that  not  one  in  ten  of 
the  young  men  and  women  who  learn  to  repeat  this 
statement  at  our  high  schools  and  academies  have 
any  clear  idea  of  what  it  means.  For  many  years 
I  have  asked  questions  on  the  examination  papers 
for  admission  to  Harvard  College  to  test  this  very 
point,  and  it  has  been  the  rarest  exception  to  re- 
ceive an  intelligent  answer.  Although  I  have  re- 
peated the  same  question  year  after  year,  the  result 
has  been  uniformly  unsatisfactory;  and  not  until  ex- 
perimental teaching  was  introduced  into  some  of  the 
preparatory  schools  was  there  any  improvement. 
To  most  of  the  men  the  names  oxygen  and  hydrogen 
conveyed  no  conception  of  definite  substances ;  and  in 
what  sense  it  could  be  said  that  the  familiar  liquid 
water  was  composed  of  two  aeriform  substances,  and 
on  what  evidence  this  remarkable  scientific  conclu- 
sion is  based,  almost  no  one  had  clear  ideas.  The 
laboratory  student,  however,  who  has  actually  made 
oxygen  and  hydrogen  gases  from  water,  and  who  has 


NATURE   THE   ONLY  AUTHORITY.  1 99 


satisfied  himself  with  this  evidence  that  these  aeriform 
products  came  from  the  material  of  water  and  from 
nothing  else ;  who  also  has  mixed  two  volumes  of 
hydrogen  gas  with  one  volume  of  oxygen  gas,  and 
after  exploding  the  mixture  with  an  electric  spark 
has  seen  that  the  result  is  two  volumes  of  vapor 
which  condense  on  cooling  into  liquid  water,  and 
must  therefore  be  steam,  —  has  a  knowledge  of  a 
wholly  different  kind.  He  knows  that  the  conclusion 
so  tersely  stated  in  his  text-book  is  far  from  self-evi- 
dent; he  has  experienced  the  difficulties  which  had 
to  be  overcome  before  the  truth  was  established ;  he 
has  seen  the  limitations  under  which  this  truth  must 
be  held ;   and  his  knowledge  is  complete  and  final. 

In  literature  the  printed  record  is  the  final  appeal ; 
but  in  science  books  are  at  best  only  a  secondary 
authority,  and  can  never  supply  the  place  of  direct 
observation  and  experiment.  All  descriptions  of 
natural  phenomena  are  necessarily  partial  and  im- 
perfect; and  in  elementary  works  they  are  as  a  rule 
so  inadequate  as  to  be  constantly  misleading.  Any 
one  who  relies  upon  them  is  liable  to  be  led  into 
serious  error.  Hence  it  is  that  students  of  nature 
often  hold  in  such  slight  esteem  popular  expositions 
of  scientific  subjects,  feeling  that  they  often  convey 
false  impressions  and  inculcate  error  in  spirit,  if  not 
in  substance.  Nevertheless,  such  popular  expositions 
have  their  proper  place,  and  are  of  the  greatest  im- 
portance, not  only  by  awakening  interest  in  scientific 
subjects  but  also  by  exhibiting  large  views  of  scien- 
tific relations.  They  are  avenues  to  knowledge  which 
men  may  wisely  follow,  and  by  which  many  have  been 
14 


200  EDUCATIONAL  NEEDS. 


led  into  the  sanctuaries  of  truth  ;  but  the  scholar  must 
worship  at  the  shrine  and  wait  on  the  altars,  if  he 
would  interpret  the  oracles  aright. 

One  of  the  great  educational  needs  of  our  day  is 
such  a  training  by  the  schools  in  experimental 
methods  as  will  enable  the  great  body  of  our  edu- 
cated men  to  weigh  scientific  evidence,  and  thus  to 
protect  the  community  from  the  frauds  and  sophis- 
tries of  which  otherwise  intelligent,  instructed,  and 
even  shrewd  men  are  now  so  frequently  the  dupes. 
Of  the  common-school  system,  so  early  established 
and  carefully  fostered  by  our  forefathers,  we  are  justly 
proud;  but  let  us  not  be  blind  to  the  fact  that  this 
system  has  grave  defects,  and  has  been  excelled  in 
several  countries  whose  governments  entered  on  the 
great  work  of  popular  education  long  after  ourselves. 
In  many  respects  our  methods  of  elementary  educa- 
tion are  inferior  to  those  of  Germany,  of  Sweden,  or 
of  Italy.  Two  very  obvious  reasons  may  be  assigned 
for  this  result.  In  the  first  place,  the  details  of  our 
system  are  ordered  by  the  average,  and  not  by  the 
highest  intelligence  of  the  community;  and  in  the 
second  place,  our  school  boards  are  greatly  hampered 
in  all  efforts  for  reform  by  the  cost  of  labor. 

The  ingenuity  of  our  people  has  not  failed  to  devise 
expedients  for  economizing  the  labor  of  the  teacher, 
and  thus  for  enabling  one  man  to  control  the  greatest 
possible  number  of  pupils.  In  almost  every  subject 
taught  in  our  secondary  schools  books  are  provided 
in  which  each  day's  lesson  is  exactly  proportioned, 
and  the  questions  to  be  asked  definitely  appointed. 
The  teacher's  work  is  made  as  mechanical  as  possible, 


MECHANICAL  TEACHING.  201 

and  the  pupil's  task  becomes  a  mere  exercise  of  the 
memory.  Under  such  conditions  there  is  no  need 
that  a  teacher  should  have  any  special  knowledge 
of  the  subject  taught ;  and  untrained  persons  are  em- 
ployed, whose  whole  knowledge  of  the  subject  is 
bounded  by  the  covers  of  a  school-book;  which  too 
often  has  been  prescribed  by  a  school  committee, 
under  the  influence  of  interested  publishers.  Thus 
education  is  cheapened  in  our  country,  like  so  many 
other  products  of  labor,  at  the  expense  of  refinement 
and  finish. 

It  is  no  wonder  that  the  overworked  and  under- 
paid teachers  should  oppose  any  change  which  neces- 
sarily involves  a  large  increase  of  labor,  even  when 
they  fully  recognize  the  ruinous  effects  of  the  me- 
chanical system  under  which  they  are  compelled 
to  work.  Obviously,  however,  this  substitution*  of 
indiscriminate  cramming,  in  place  of  intelligent  acqui- 
sition is  fatal  to  the  efficiency  of  our  school  system, 
and  a  reform  should  be  demanded  at  any  cost. 

Fortunately,  our  political  system  is  as  flexible  as  it 
is  crude ;  and  if  the  demand  is  seriously  made  the 
reform  is  sure  to  follow.  But  let  it  be  remembered 
that  the  changes  required  will  be  necessarily  costly, 
and  we  must  be  prepared  to  bear  the  increased  ex- 
pense. Do  not,  however,  be  deceived  by  any  make- 
shifts which  are  often  paraded  as  scientific  education. 
If  teaching  is  to  be  simply  a  process  of  loading  the 
memory  with  more  or  less  useful,  as  well  as  more  or 
less  ephemeral,  information  it  makes  little  difference 
in  the  end  what  are  the  materials  used  in  the  process 
of  cramming.     The  material  may  as  well  be  the  long 


202       CONDITIONS    OF   SUCCESSFUL   TEACHING. 

list  of  exceptions  to  the  rules  of  prosody,  required  in 
the  Latin  schools  of  former  days,  as  descriptions  of 
experiments  in  physics  or  chemistry  so  glibly  recited 
by  the  pupils  of  our  modern  high  schools. 

No  teaching  of  science  is  of  any  value  which  is  not 
a  direct  appeal  from  the  mind  of  the  teacher  to  the 
intelligence  of  the  pupil.  The  teaching  must  be 
direct  and  personal,  and  this  necessarily  implies  a 
large  expenditure  of  time  and  patience,  a  special 
training  on  the  part  of  the  teacher,  and  a  great 
increase  of  teaching  force. 

The  successful  teaching  of  natural  science  also 
requires  that  the  teacher  should  be  independent  of 
all  books.  The  great  object  of  science-training  is  to 
enable  the  scholar  to  interpret  nature;  and  the  book 
of  nature  is  the  only  text-book  which  should  be  pre- 
scribed. As  in  the  study  of  ancient  classics  the  one 
great  aim  is  to  acquire  such  a  command  of  Latin  or 
Greek,  such  a  knowledge  of  the  circumstances  and 
relations  of  these  elder  nations,  as  will  enable  the 
student  to  render  not  only  the  general  sense,  but  also 
the  delicate  shades  of  meaning  and  the  coloring  of 
the  language  of  their  writers;  so  in  the  study  of 
science  the  great  object  is  to  interpret  the  meaning 
of  natural  phenomena,  to  decipher  the  significance 
of  every  feature,  and  to  show  forth  the  intelligence  of 
which  nature  is  the  expression. 

Books  have  their  value  chiefly  as  guides,  and  as 
records  of  what  has  already  been  accomplished ;  but 
in  the  study  of  nature  they  hold  a  secondary  and 
subordinate,  and  not  a  chief  place.  To  train  young 
minds    to    interpret   nature    is   a    perfectly    practical 


THE  TRUE  AIM.  203 


scheme.  The  power  can  be  acquired  as  readily  as 
the  ability  to  translate  Virgil  or  Homer,  although  of 
course  with  limitations  which  are  similar  in  both 
cases ;  and  it  is  this  power,  and  not  the  mere  acqui- 
sition of  scientific  knowledge,  at  which  the  so-called 
"  new  education "  aims.  This  all-important  state- 
ment cannot  be  too  often  repeated,  or  too  strongly 
emphasized.  The  advocates  of  an  exclusively  clas- 
sical culture  constantly  describe  the  new  education 
as  an  attempt  to  substitute  the  acquisition  of  useful 
knowledge  for  mental  discipline;  or,  at  best,  to  re- 
place serious  intellectual  work  with  superficial  object- 
teaching;  and,  as  we  have  before  intimated,  there 
has  been  an  attempt  on  the  part  of  some  schools  to 
satisfy  an  obvious  demand  with  such  contemptible 
shifts.  Let  me  then  repeat  that  the  great  aim  of  sci- 
entific training  should  be  the  ability  to  interpret 
nature ;  and  that  in  large  measure  the  acquisition  is 
within  the  reach  of  every  educated  man,  although 
in  its  higher  manifestations  the  successful  exercise 
of  this  ability  may  be  a  privilege  of  only  the  most 
gifted  intellects. 

That  such  training  is  of  the  highest  value  and  is  a 
legitimate  aim  of  education,  must,  I  think,  be  univer- 
sally admitted;  but  it  cannot  be  secured  without 
trained  teachers,  without  well-appointed  laboratories, 
and  except  at  a  cost  proportionate  to  such  require- 
ments. Certainly  we  cannot  afford  to  fall  behind  the 
most  favored  nations  of  the  earth  on  the  very  ground 
which  we  first  occupied  ;  and  it  is  equally  certain  that 
no  investment  will  yield  a  larger  return  than  the  money 
expended  in  the  acquisition  of  real  knowledge. 

The  distinction  between  real  knowledge  and  formal 


204  REAL   AND    FORMAL   KNOWLEDGE. 


knowledge  is  one  of  paramount  importance,  which 
should  never  be  overlooked  in  our  plans  of  educa- 
tion. That  knowledge  alone  is  real  to  a  student 
which  is  obviously  related  to  some  need  of  his  life, 
or  to  some  phase  of  his  intelligence.  All  other 
knowledge,  however  valuable  in  itself  considered,  is 
to  him  formal.  Obviously,  the  distinction  here  in- 
sisted on  is  purely  a  relative  one;  for  the  same 
knowledge  which  is  formal  to  one  man  may  be  very 
real  indeed  to  his  next-door  neighbor.  The  para- 
digms of  grammar  are  formal  knowledge  to  the  young 
student  who  memorizes  them  for  the  first  time,  but 
are  very  real  knowledge  to  the  grammarian.  Even 
formal  knowledge  has  its  right  place ;  and  there  are 
exigencies  under  which  its  acquisition  is  to  be  en- 
couraged or  even  enforced.  Man  is  a  creature  of 
habit,  and  his  usefulness  requires  that  certain  essen- 
tial truths  should  become  so  woven  into  his  nature  as 
to  be  always  at  hand  on  every  emergency.  Certainly 
the  multiplication-table  and  the  spelling-book  repre- 
sent formal  knowledge  of  this  sort;  but  I  do  maintain 
that  it  should  be  the  great  object  of  education  to  re- 
late all  knowledge,  so  far  as  possible,  to  the  pupil's 
understanding. 

I  know  that  on  this  point  I  differ  from  many  old 
experienced  teachers  whom  I  greatly  respect.  It  was 
formerly  held  almost  universally,  and  even  now  it  is 
believed  by  many  teachers,  to  be  best  for  a  child  to 
acquire  knowledge  at  first  in  a  formal  way,  and  to 
wait  for  the  development  of  his  intelligence  to  ex- 
hibit its  relations.  On  this  theory,  boys  preparing 
for  college  in  my  own  school-days  were  compelled  to 


REAL  AND   FORMAL   KNOWLEDGE.  205 

> . 

learn  the  Latin  grammar  by  rote  before  they  under- 
stood the  meaning  of  one  half  of  the  terms  employed. 
The  vivid  remembrance  of  my  own  experience  may 
lend  undue  proportions  to  this  abuse  of  the  memory; 
still,  after  a  long  experience  as  a  teacher  myself,  I 
cannot  but  regard  such  discipline  as  a  great  waste  of 
mental  energy,  if  not  absolutely  cruel ;  and  no  one 
can  deny  that  the  acquisition  of  any  knowledge  is 
greatly  facilitated  when  the  relations  of  the  knowledge 
are  understood.  I  have  granted  that  in  certain  cases 
the  acquisition  of  formal  knowledge  is  necessary;  nev- 
ertheless, it  should  be  the  study  of  the  teacher  to  les- 
sen the  requirement  as  far  as  possible ;  and  certainly  in 
science,  formal  knowledge  is  wholly  without  value. 

Some  years  ago,  while  working  in  the  mineralogical 
cabinet  under  my  charge  at  Cambridge,  I  was  ad- 
dressed by  two  lady  visitors  who  had  evidently  found 
great  interest  in  the  collection,  and  asked  some  very 
intelligent  questions  in  regard  to  several  of  the  more 
common  mineral  species.  It  gave  me  great  pleasure 
to  answer  their  inquiries,  and  I  passed  a  pleasant 
hour  in  pointing  out  some  of  the  characteristic  feat- 
ures of  quartz,  feldspar,  mica,  pyroxene,  hornblende, 
and  similarly  familiar  minerals  which  are  the  constitu- 
ents of  our  common  rocks.  At  the  close  of  this  im- 
provised lecture,  one  of  the  ladies  said  to  me  in  an 
apologetic  tone,  —  evidently  deeming  some  excuse  re- 
quired for  such  an  unusual  feminine  taste,  —  "  We  are 

teachers  in  the  High  School,"  naming  a  town 

not  one  hundred  miles  distant  from  Boston,  "  and  I 
have  been  taking  a  class  through  the  sections  on 
mineralogy,  introductory  to  Dana's  Geology ;   and  I 


206  REAL  AND   FORMAL   KNOWLEDGE. 


was  interested  to  see  some  of  the  minerals  described 
in  them." 

I  think  this  incident,  without  further  comment,  will 
illustrate  what  I  mean  by  a  formal  knowledge  of  ele- 
mentary science,  and  will  also  show  how  utterly  worth- 
less all  such  acquisition  must  be.     The  incident  has 
an  amusing  side,  but  it  also  exhibits  a  very  sad  aspect 
of  our  secondary  education.     This  lady  was  evidently 
a  conscientious   teacher,  who   had   a  conception   of 
something  better  than  the  mechanical  routine  in  which 
she  was  forced  to  work,  and  this  had  led  her  to  seek 
some  real  knowledge  of  the  subject  she  had  to  teach. 
I  know  that  there  has  been  a  great  improvement  in 
our  schools  during  the  last  few  years ;   and  the  prac- 
tical classes  supported  by  the  Lowell  Fund,  under  the 
direction  of  the  teachers  of  the  Boston  Institute  of 
Technology,  as  well  as  similar  courses  under  the  aus- 
pices of  the  adjacent  Natural  History  Society,  have 
done  not  a  little  to  hasten  the  reform.     But  our  best 
teachers  are  still  constrained  by  over-crowded  class 
rooms,  and  the  mechanical  routine  which  this  condition 
of  things  necessarily  implies.    Of  this  I  know.     There 
is  not  a  more  devoted  or  more  conscientious  class  of 
workers  in  our  community  than  the  teachers  of  the 
secondary  schools ;    and  if  our  people  realized  how 
much  mental  energy  was  wasted  in  these  schools  by 
just  such  senseless  tasks  as  attempting  to  teach  min- 
eralogy from  a  book,  the  teachers  would   soon  be 
relieved  from  such  profitless  and  thankless  duties. 

What  I  have  said  in  regard  to  the  teaching  of 
science,  applies  with  almost  equal  force  to  literary 
studies  as  well.     Real  knowledge  has  the  same  great 


REAL  AND   FORMAL   KNOWLEDGE.  207 

worth  in  every  department  of  learning,  and  formal 
teaching  the  same  deadening  influence ;  and  let  it 
not  be  inferred  from  anything  I  have  said,  that  I 
desire  to  exalt  scientific  culture  at  the  expense  of 
literary  or  artistic  culture  of  any  kind.  All  mental 
culture  is  alike  good ;  and  it  is  not  by  a  one-sided 
growth,  but  by  a  symmetrical  development  of  all  its 
powers,  that  a  community  can  secure  the  largest 
productiveness  and  acquire  the  widest  influence. 

I  have  elsewhere  expressed  myself  so  strongly  on 
this  point  that  it  does  not  seem  to  me  necessary  that 
I  should  guard  the  language  here  used  against  any 
misinterpretation  ;  but  that  I  may  make  the  dec- 
laration still  more  emphatic,  let  me  repeat  that  I 
still  believe  the  old  forms  of  literary  culture  to  be 
for  the  large  majority  of  scholars  the  best  prepara- 
tion for  useful  lives.  I  merely  claim  that  there  is  an 
important  class  of  the  students  who  now  seek  a  col- 
lege education,  for  whom,  on  the  other  hand,  a  sci- 
entific culture  will  best  secure  their  future  usefulness ; 
and  I  have  already  indicated  sufficiently  clearly  what 
I  mean  by  scientific  culture  in  this  connection.  Let 
not  scientific  culture  be  confounded  with  technical 
training,  and  let  it  not  be  misjudged  by  any  counter- 
feits which  have  assumed  its  name.  Several  of  the 
sciences  have  opened  lucrative  fields  for  professional 
labor;  and  the  engineer,  the  chemist,  and  the  electri- 
cian follow  as  learned  vocations  as  the  lawyer  or  the 
physician.  For  each  of  these  new  professions,  as 
for  those  of  the  elder  triad,  special  training  is  re- 
quired;  and  in  all  of  them  some  of  the  subjects 
involved  are  the  same  as  those  studied  in  view  solely 


208      TECHNICAL  TRAINING  AND   LIBERAL   CULTURE. 


of  a  general  education.  The  difference  between 
technical  training  and  liberal  culture  depends,  not 
chiefly  on  the  subject-matter  studied,  but  on  the 
purposes  and  spirit  with  which  the  study  is  pursued. 
Thus,  chemistry  studied  with  the  object  of  manufac- 
turing chemical  products,  or  of  directing  other  chem- 
ical industries,  or  of  solving  the  numerous  sanitary 
and  technical  problems  which  constantly  arise  in 
every  highly  civilized  community,  is  a  legitimate 
and  learned  profession ;  but  when  studied  for  the 
sole  object  of  interpreting  nature  and  extending 
knowledge,  it  is  one  of  the  liberal  arts.  I  do  not 
say  that  one  object  is  more  worthy  or  more  noble 
than  the  other ;  but  I  do  maintain  that  any  country 
becomes  more  enlightened  and  more  honored  in 
proportion  as  liberal  culture  is  fostered  and  main- 
tained. That  it  will  have  its  proper  place  in  our 
community  is  already  assured ;  and  the  movement 
recently  inaugurated  by  Harvard  College  is  already 
producing  visible  effects. 

To  this  reform  in  education,  and  to  the  substitu- 
tion of  real  for  formal  knowledge  which  it  involves, 
I  look  more  than  to  anything  else  for  the  reconcilia- 
tion between  science  and  theology.  When  all  the 
wisdom  and  learning  of  this  world  has  been  related 
not  only  to  man's  need  of  beauty  and  to  man's  need 
of  conduct,  but  also  to  man's  need  of  understanding 
and  man's  need  of  religion,  the  harmony  between 
material  and  spiritual  truths  will  plainly  appear;  and 
thus  it  is  that  this  discussion  of  what  seemed  at  first 
a  purely  educational  problem,  has  an  important 
bearing  on  the  larger  subject  we  have  in  hand. 


THE   MEANING   OF   LAWS.  20O. 


LECTURE   VIII. 

THEORIES    OR   SYSTEMS    OF   SCIENCE. 

IN  my  last  lecture  I  defined  a  law  of  nature  as  a 
declaration  or  statement  of  a  certain  order,  se- 
quence, or  relation  observed  among  natural  phenom- 
ena, and  aimed  to  show  that  such  propositions  could 
be  regarded  from  no  point  of  view  as  efficient  causes. 
It  is  not  in  the  study  of  nature  alone  that  the  mind 
of  man  does  not  rest  satisfied  with  laws.  In  social 
relations  as  well  as  in  science,  men  demand  to  know 
the  meaning  of  laws,  and  their  demands  are  the  more 
imperative  in  proportion  as  they  become  more  en- 
lightened. The  scientific  investigator  is  not  con- 
tent with  a  knowledge  of  the  outward  relations  of 
phenomena.  He  seeks  to  discover  the  proximate 
causes  of  the  order  he  has  observed,  and  although 
he  may  not  be  able  to  reach  certainty,  he  is  not 
satisfied  until  he  has  framed  some  explanation  by 
which  he  can  classify  his  facts,  and  which  at  the  same 
time  will  give  the  form  and  body  to  his  thoughts 
so  indispensable  for  successful  study.  Hence  arise 
of  necessity  the  hypotheses,  theories,  and  systems  of 
science. 

Using  the  term  in  its  broadest  sense,  an  hypothesis 
is  a  postulate  imagined  or  assumed  to  account  for 


2IO  H\TOTHESIS. 


what  is  not  understood.  Its  derivative  meaning  from 
vTTodeo-Ls  (a  supposition)  is  closely  followed  in  the 
meaning  here  assigned  to  the  word.  These  suppo- 
sitions may  be  based  on  a  larger  or  smaller  knowl- 
edge, they  may  be  more  or  less  in  harmony  with  nat- 
ural phenomena,  they  may  more  or  less  fully  agree 
with  generally  accepted  systems  of  science ;  but  they 
differ  from  the  laws  of  nature  in  that  they  seek  to  go 
behind  the  external  relations  of  things,  and  explain 
how  this  order  might  have  been  produced.  The 
word  "  hypothesis,"  unfortunately  for  our  purpose, 
has  acquired  a  coloring  which  suggests  a  deprecia- 
tory inference.  A  plausible  supposition  is  sometimes 
spoken  of  contemptuously  as  "  a  mere  hypothesis ;  " 
and  possibly  for  this  reason  the  term  "  theory,"  al- 
though often  branded  in  a  similar  way,  is  frequently 
used  by  scientific  writers  to  distinguish  such  hypoth- 
eses as  they  regard  as  more  credible  or  more  fully 
established.  But  until  the  truth  of  an  hypothesis 
has  been  placed  beyond  doubt,  —  when  of  course  it 
ceases  to  be  a  supposition,  and  is  classed  among 
fixed  facts, — the  degree  of  credibility  must  be  to  a 
great  extent  a  matter  of  opinion,  and  no  definite  line 
of  distinction  can  be  drawn.  Moreover,  the  word 
"  theory "  has  a  very  important  use,  corresponding 
also  to  its  derivation,  which  we  cannot  afford  to  have 
compromised.  We  shall  use,  therefore,  the  word 
"  hypothesis  "  to  designate  any  assumed  explanation 
of  natural  phenomena,  without  any  implication  as  to 
the  plausibility  of  the  supposition. 

As  is  well  known,  it  is  a  fundamental  doctrine  of 
the  positive  philosophy  that  man  can  know  nothing 


MAN'S  DISCERNMENT,  AND   GOD'S  INSPIRATION.      211 

of  efficient  causes.  Hence  all  hypotheses  are  vani- 
ties, and  the  only  reasonable  course  for  helpless  man 
is  to  limit  his  attention  to  determinate  relations  of 
phenomena ;  that  is,  to  natural  laws.  But  this  phil- 
osophy utterly  ignores  the  only  power  by  which  the 
level  of  human  knowledge  can  be  raised ;  that  is,  in- 
duction :  and  as  we  have  shown  in  previous  lectures, 
the  whole  history  of  science  is  simply  the  story  of 
verified  inductions.  Guesses  at  truth  are  not  to  be 
despised,  for  they  have  been  again  and  again  divina- 
tions. 

We  cannot  expect  fruitful  suggestions  except  from 
men  who  are  thoroughly  acquainted  with  the  subject 
they  are  studying;  but  to  gain  any  insight  into 
nature's  processes,  something  more  than  erudition  is 
required;  call  it  genius,  call  it  intuition,  call  it  in- 
spiration, or  by  whatever  other  name,  there  is  an 
element,  although  we  may  not  be  able  to  define  it 
precisely,  which  we  all  recognize  in  such  creative 
minds.  Man's  discernment  and  God's  inspiration 
blend  together,  and  no  one  can  distinguish  the  point 
where  they  meet. 

There  is  a  certain  sense  in  which  the  suggestions 
of  gifted  minds  maybe  said  to  be  the  oracles  of  God  ; 
and  there  is  another  sense  in  which  they  must  be 
regarded  as  the  conceits  of  very  fallible  and  short- 
sighted men;  and  it  is  no  wonder  that  their  value 
will  be  very  differently  estimated  according  as  they 
are  regarded  from  one  or  the  other  point  of  view.  I 
have  the  greatest  respect  for  the  love  of  truth  and 
accuracy  which  the  positive  philosophy  so  strongly 
inculcates ;  but,  as  it  seems  to  me,  this  doctrine  finds 


212      SYMPATHY   BETWEEN   MIND   AND   NATURE. 

its  chief  disciples  among  scholars  who  have  been  so 
engrossed  in  deductive  methods  as  to  overlook  the 
mental  visions  by  which  the  broader  relations  of  truth 
have  been  discovered. 

To  my  mind  there  is  a  deeper  and  nobler  philoso- 
phy than  positivism,  which  explains  that  mysterious 
sympathy  between  mind  and  nature  so  evident  in  the 
great  discoverers,  —  a  philosophy  proclaimed  in  the 
declaration  of  Holy  Scripture  that  man  was  created 
in  the  image  of  God.  Only  in  proportion  as  man  par- 
takes of  the  Divine  intelligence  can  he  understand  the 
Divine  creation,  and  just  in  proportion  as  he  is  in 
sympathy  with  the  Divine  mind  will  he  recognize  the 
Divine  thought  which  has  been  manifested  in  nature. 
And  even  if  we  take  no  higher  view  than  that  man 
has  grown  into  harmony  with  his  environments 
through  the  influence  of  what  is  called  natural  selec- 
tion, we  must  at  least  recognize  in  such  antecedents 
a  close  relationship  with  the  rest  of  nature ;  and  this 
affinity  alone  would  help  to  explain  the  power  of 
genius  to  frame  fruitful  hypotheses. 

As  we  have  already  explained,  there  is  but  one  sat- 
isfactory test  of  the  Divine  afflatus  in  such  imagin- 
ings ;  and  that  is  the  test  of  experience.  Hypothesis 
is  of  value  only  in  so  far  as  it  explains  facts,  and  by 
pointing  out  consequences  directs  investigation,  —  as 
has  been  already  fully  illustrated.  In  this  way  hypo- 
theses have  been  the  chief  means  by  which  science 
has  been  advanced.  The  great  discoverers  have  been 
the  men  who  were  the  most  fruitful  in  hypotheses, 
and  at  the  same  time  most  skilful  and  conscientious 
in  submitting  them  to  the  test  of  observation  and  ex- 


THEORIES   OF   SCIENCE.  213 

periment,  —  men   like    Copernicus,    Kepler,    Galileo, 
Huygens,  Newton,  Oersted  and  Faraday. 

I  have  already  shown  out  of  what  copious  and  often 
grotesque  fancies  the  laws  of  Kepler  were  educed; 
and  Faraday,  although  far  more  sober-minded,  was 
equally  distinguished  by  exuberance  of  fancy;  but, 
like  Kepler,  he  submitted  his  hypotheses  to  the 
severest  tests.  So  also  Newton,  while  emphatically 
expressing  his  contempt  for  idle  speculations  in  his 
celebrated  aphorism  already  quoted,  constantly  made 
use  of  legitimate  hypotheses  in  his  own  investiga- 
tions,—  as  both  his  "Optics"  and  his  "  Principia  " 
give  abundant  evidence. 

The  word  "  theory  " —  from  Oewpeay,  to  see  or  con- 
template—  is  correctly  used  in  speaking  of  a  system 
of  science,  as  the  theory  of  music,  or  the  theory  of  the 
moon;  and  to  this  meaning  it  is  best  limited.  In 
this  sense  a  theory  may  involve  many  principles  and 
complex  relations.  It  may  be  based  on  known  laws 
or  definite  facts,  as  is,  for  example,  the  theory  of 
sound ;  or  it  may  rest  to  a  greater  or  less  extent  on 
hypotheses,  as  does  the  undulatory  theory  of  light  on 
the  assumption  of  an  adamantine  ether.  It  is  there- 
fore plainly  to  be  distinguished  on  the  one  hand  from 
a  law,  which  is  the  declaration  of  known  relations,  and 
on  the  other  hand  from  an  hypothesis,  which  is  an 
assumption  of  unknown  conditions.  Indeed,  it  often 
includes  both  laws  and  hypotheses,  and  attempts  to 
correlate  them  in  a  consistent  system.  The  theories 
of  science  are  of  the  very  greatest  value,  and  chiefly 
in  two  ways. 

In  the  first  place,  a  good  theory  has  a  very  great 


214  VALUE   OF  THEORIES. 

educational  value.  It  classifies  facts,  it  unfolds  phe- 
nomena in  logical  sequences,  and  exhibits  events  in 
intelligible  relations.  As  thus  presented,  the  mind  is 
able  to  grasp  the  subject  as  a  whole,  to  view  it  in 
many  relations,  and  through  their  relationships  to 
gain  a  command  of  a  mass  of  facts  which  otherwise 
the  most  retentive  memory  could  not  hold.  We  are 
all  acquainted  with  this  use  of  theory.  We  know 
how  completely  our  working  knowledge  in  almost 
any  department  of  learning  is  associated  with  the 
system  in  which  it  was  acquired,  and  many  of  us 
know  by  experience  how  difficult  it  is  to  work  with  a 
new  system  when  the  progress  of  knowledge  demands 
a  change.  Theories  are  thus  necessities  of  our  men- 
tal constitution,  and  essential  conditions  of  effective 
thought. 

In  the  second  place,  theories  are  of  the  very  great- 
est use  in  directing  investigation,  and  in  natural  science 
their  efficiency  in  this  respect  is  their  chief  merit. 
The  highest  recommendation  we  can  give  to  a  system 
of  science  is  to  say  that  it  is  a  good  working  theory; 
and  in  saying  this  we  do  not  necessarily  pass  any 
judgment  on  the  credibility  of  the  system  as  abstract 
truth.  As  I  shall  soon  show,  we  have  good  working 
theories  whose  postulates  cannot  for  a  moment  be 
regarded  as  realities ;  but  so  long  as  the  theories 
direct  us  to  new  discoveries  it  would  be  the  height  of 
folly  to  abandon  them  simply  because  they  cannot  be 
squared  with  our  speculative  philosophy.  There  has 
been  a  great  deal  of  misunderstanding  on  this  point 
which,  in  the  interest  both  of  religion  and  of  sound 
philosophy,   ought   to  have   been    avoided.      Sober- 


RESERVATION   OF  JUDGMENT.  21$ 

minded  men  have  been  accused  again  and  again  of 
being  false  to  religion  because  they  entertained  theo- 
ries which  the  Church  at  the  time  regarded  as  incon- 
sistent with  sound  doctrine ;  and,  in  defending  their 
position,  I  have  known  men  of  great  power  driven 
into  extreme  positions  by  an  intolerance  which  forced 
a  mental  conflict  where  none  need  to  have  followed. 
If  in  the  study  of  nature  there  is  one  truth  more  than 
another  which  it  is  important  for  the  student  to  learn, 
it  is  that  in  a  great  many  cases  reservation  of  judg- 
ment is  the  only  honest  attitude  of  the  mind ;  and 
that  man  is  to  be  honored,  and  not  persecuted,  who 
can  use  his  theories  for  what  they  are  worth  and 
keep  his  faith  in  eternal  verities  pure  and  radiant. 

As  we  cannot  expect  a  theory  fully  to  harmonize 
with  our  philosophy,  so  we  cannot  expect  that  its 
predictions  will  always  be  verified.  Of  course  the 
failure  of  a  theory  to  account  for  well-established 
phenomena  shows  that  either  the  theory  or  our 
powers  of  deduction  must  be  at  fault;  but  this  is  no 
reason  for  rejecting  the  system,  until  we  can  find  a 
better  theory  to  take  its  place.  How  foolish  it  would 
have  been  for  Columbus  to  throw  overboard  his  com- 
pass-needles when  he  discovered  that  they  did  not 
point  exactly  to  the  north  star.  Like  all  human  in- 
ventions, systems  of  science  are  imperfect;  and  we 
must  accept  them  for  what  they  are  worth,  and  use 
them  only  so  long  as  they  give  us  essential  help  in 
our  search  for  knowledge.  It  has  been  repeatedly 
the  case  in  the  history  of  science,  that  theories  have 
failed  so  completely  to  do  their  legitimate  work  that 
they  have  been  deposed  and  new  theories  enthroned 
15 


2l6  HYPOTHETICAL   MAGNITUDES. 

in  their  place;  but  so  intimately  are  theories  asso- 
ciated with  our  processes  of  thought,  that  the  change 
has  usually  been  attended  with  an  intellectual  revolu- 
tion. As  I  have  shown  in  these  lectures,  it  was  so 
when  the  Ptolemaic  theory  was  set  aside  ;  and  we 
have  had  a  similar  experience  in  chemistry  since  I 
have  been  a  teacher  of  the  science. 

We  have  said  that  a  system  of  science  might  in- 
volve postulates  wholly  inconsistent  with  sound  phil- 
osophy, and  yet  remain  a  good  working  theory;  we 
have  now  to  add,  what  is  still  more  surprising,  that 
such  a  theory  may  give  us  accurate  measurements  of 
magnitudes  which  are  wholly  hypothetical,  and  of 
whose  relations  we  have  otherwise  no  positive  knowl- 
edge. Such,  for  example,  are  the  absolute  lengths 
of  the  so-called  waves  of  light,  and  the  relative 
weights  of  the  chemical  molecules  and  atoms.  There 
cannot  be  a  question  that  the  values  obtained  are 
real  magnitudes;  and,  although  we  have  made  our 
measurements  in  the  dark  and  have  not  known  cer- 
tainly what  we  were  measuring,  yet  the  definiteness 
of  the  results  gives  us  the  strongest  assurance  that 
our  theories  contain  an  element  of  truth,  although  the 
truth  may  be  clothed  with  much  error. 

We  have  already  seen  what  a  mighty  influence  the 
Ptolemaic  system  and  the  "  Organon  "  of  Aristotle 
exerted  over  the  intellectual  world  for  more  than  a 
thousand  years ;  and  at  the  present  day,  besides  the 
many  subsidiary  theories,  there  are  four  great  systems 
of  science  which  possess  a  similar  authority.  These 
are  the  Theory  of  Universal  Gravity,  the  Undulatory 
Theory  of  Light,  the  Molecular  Theory  of  Chemistry 


DOMINANT  THEORIES   OF  SCIENCE.  2iy 

and  Physics,  and  the  Theory  of  Organic  Develop- 
ment; and  I  propose  in  this  lecture  to  show  that 
these  famous  systems  of  science  exhibit  in  a  most 
striking  manner  the  characteristic  features  of  all 
human  theories  to  which  I  have  referred. 

In  my  last  lecture  I  not  only  pointed  out  the  clear 
distinction  between  the  law  of  gravitation  and  the 
theory  of  universal  gravity,  but  I  also  discussed  some 
of  the  incongruities  which  this  assumed  mode  of 
action  presents,  showing  that  the  idea  of  independent 
attractive  forces  exerted  by  separate  particles  of  mat- 
ter was  not  only  inconsistent  with  the  fundamental 
conception  of  inertia,  but  also  entirely  out  of  har- 
mony with  our  knowledge  of  other  attractive  forces, 
like  those  exerted  by  electricity  and  magnetism. 
Remember  that  each  particle  of  matter  of  this  earth 
is  assumed  to  attract  each  particle  of  the  planet 
Jupiter,  each  one  every  other,  as  if  there  were  no 
other  material  in  the  universe. 

Now  besides  the  improbability  and  incongruity  of 
such  independent  action,  the  whole  idea  is  at  utter 
variance  with  a  principle  which  in  all  philosophical 
thought  has  always  been  regarded  as  a  prime  condi- 
tion of  every  mode  of  action,  and  which  is  expressed 
in  the  aphorism  "  Nulla  actio  in  distans."  This  prin- 
ciple has  been  universally  recognized  in  other  systems 
of  science.  It  was  recognized  by  Newton  himself  in 
his  emission  theory  of  light,  which  ascribed  the  lumi- 
nous power  to  small  projectiles  darting  through  the 
intervening  space  and  carrying  the  energy  from  the 
luminous  body  to  the  point  of  application;  and  to 
these  projectiles  Newton  gave  form  and  imparted  ro- 


2l8  THEORY  OF  UNIVERSAL   GRAVITY. 

tation  in  order  to  explain  what  he  called  "  fits  of  easy 
transmission"  or  reflection.  The  same  philosophical 
necessity  for  a  medium  of  transmission  led  Huygens, 
in  framing  his  wave  theory  of  light,  to  fill  all  space 
with  an  elastic  medium,  through  which  the  waves  might 
be  propagated.  This  medium,  which  to  his  conception 
was  an  indefinitely  attenuated  but  highly  elastic  con- 
dition of  aeriform  matter,  as  its  name  denotes,  the  de- 
mands of  modern  science,  as  we  shall  soon  see,  have 
converted  into  an  adamantine  solid.  It  was  again  the 
same  necessity  of  thought  which,  in  a  most  memo- 
rable investigation,  led  Faraday  to  search  for  the 
medium  through  which  electrical  attractions  and  re- 
pulsions are  exerted,  and  to  distinguish,  as  he  did 
with  so  much  skill,  the  qualities  and  relations  of  the 
dielectric.  While,  however,  we  have  met  the  neces- 
sity by  interposing  a  medium  through  which  a  par- 
ticle of  sodium  at  the  sUn  sends  to  our  spectroscope 
an  intelligible  signal,  that  same  particle  is  assumed 
by  the  theory  of  gravitation  to  exert  an  attraction  on 
every  particle  of  that  instrument  at  the  distance  of 
ninety  millions  of  miles,  not  only  independent  of  any 
medium,  but  also  irrespective  of  any  conditions  or 
relations  except  mass. 

Although  I  feel  strongly  the  philosophical  objec- 
tion to  the  theory  of  gravitation  which  I  have  en- 
deavored to  present;  and  although  I  feel  under  the 
constraint  of  the  same  limitations  of  thought  to 
which  I  have  referred,  —  yet  sometimes  I  cannot  but 
fear  that  we  are  influenced  by  the  old  aphorism  more 
than  we  ought  to  allow  ourselves  to  be;  and  that, 
after  all,  we  may  be  but  repeating  the  experience  of 


NULLA  ACTIO   IN  DISTANS.  219 

the  Aristotleans  at  the  time  of  Galileo.  Who  can 
question  that  Nature's  abhorrence  of  a  vacuum  was 
as  much  a  philosophical  necessity  to  them  as  "  Nulla 
actio  in  distans  "  is  to  us.  Man  cannot  act  where  he 
is  not,  or  where  he  cannot  reach,  —  although  the  elec- 
trical nerves  of  modern  science  enable  him  to  reach 
across  oceans  and  continents,  and  almost  even  to 
clasp  the  globe  itself.  Moreover,  on  the  earth  we 
cannot  transmit  energy  without  an  adequate  medium. 
The  falling  water  acts  directly  on  the  turbine,  but 
power  cannot  be  transmitted  from  this  water-wheel 
to  the  spindle  and  looms  except  through  adequate 
shafting,  pulleys,  and  belts.  So  also  the  power  of 
steam,  however  far  the  steam  may  be  carried  through 
pipes,  must  do  its  work  ultimately  against  the  piston 
of  the  motor.  Even  the  more  modern  dynamo- 
machine,  by  which  power  can  be  transmitted  to 
greater  distances  than  by  any  other  means,  must 
have  a  line  of  electrical  conductors  through  which 
the  energy  passes.  In  all  these  cases  power  is  lost 
in  the  transmission  in  such  a  way  as  to  show  that  the 
transmission  takes  place  from  point  to  point  along 
the  line.  All  such  analogies  give  a  strong  support 
to  the  doctrine  that  no  action  can  take  place  except 
between  contiguous  masses;  but  should  we  not  be 
careful  not  to  limit  in  our  thoughts  the  possibilities 
of  nature  by  our  own  experience?  It  seems  to  me 
that  such  an  attitude  of  the  mind  is  required  by 
philosophical  sobriety;  and  although  I  have  given 
a  very  different  interpretation  to  the  seeming  non- 
conformity, it  is  possible  that  gravitation  is  the  first 
exceptional  phenomenon  which  has  shown  the  short- 


220  UNDULATORY   THEORY   OF   LIGHT. 

sightedness  of  our  philosophy.  Still  the  main  fact 
which  I  have  been  endeavoring  to  illustrate  remains. 
This  grand  theory  of  universal  gravitation,  from 
which  has  been  developed  the  wonderful  deduc- 
tions of  modern  astronomy,  presents  anomalies  which 
our  philosophy  has  been  wholly  unable  to  reconcile. 

Of  the  four  great  theories  of  modern  science,  the 
one  which  is  to  me  the  most  fascinating  is  the  un- 
dulatory  theory  of  light.  As  a  student  of  crystallo- 
graphy and  of  crystal  optics,  I  have  been  charmed 
by  the  completeness  with  which  it  not  only  explains 
the  general  order  of  these  phenomena,  but  also  pre- 
dicts the  magnitude,  intensity,  and  other  relations  of 
each  minute  detail.  Moreover,  the  remarkable  pre- 
diction of  conical  fraction  first  made  known  on  theo- 
retical grounds  by  Hamilton,  and  afterwards  verified 
by  Lloyd,  will  always  be  cited  as  one  of  the  most 
striking  examples  of  the  prescience  of  physical  sci- 
ence. Nevertheless,  in  spite  of  all  its  elegance  and 
efficiency,  the  undulatory  theory  of  light  is  imperfect, 
and  demands  postulates  which  even  the  wildest  im- 
agination cannot  reconcile  with  common-sense. 

The  earlier  exposition  of  the  undulatory  theory 
was  published  by  Huygens  nearly  contemporane- 
ously with  that  of  the  emission  theory  by  Newton ; 
but  although  from  the  first  much  more  elegant  in 
mathematical  form,  the  theory  of  waves  did  not  for 
a  long  time  acquire  nearly  as  great  authority  as  the 
theory  of  corpuscles ;  and  even  down  to  the  middle 
of  this  century  the  two  theories  were  described  as 
rival  systems  in  most  text-books  on  optics.  Sir 
David  Brewster,  one  of  the  most  successful  students 


NEWTON   AND   HUYGENS.  221 


of  optics  in  this  century,  who  died  in  1868,  defended 
the  Newtonian  theory  to  the  last.  Unquestionably, 
the  paramount  authority  of  Newton  in  astronomy 
gave  greater  weight  to  his  hypothesis  in  optics  than 
it  intrinsically  merited  ;  for  there  are  not  to  be 
found  in  the  whole  history  of  science  more  elegant 
demonstrations  than  those  which  Huygens  originally 
gave,  deducing  the  fundamental  principles  of  optics 
from  the  theory  of  the  wave  motion,  —  such  principles, 
for  example,  as  the  rectilinear  path  of  a  beam  of 
light,  the  laws  of  reflection  and  refraction,  and  above 
all,  the  phenomena  of  double  refraction,  then  recently 
observed  by  Erasmus  Bartolinus  in  Iceland  spar. 

Huygens  was  undoubtedly  led  to  his  wave  theory 
by  the  analogy  which  the  phenomena  of  light  and 
sound  exhibit,  and  conceived  of  waves  of  light  as 
transmitted  like  waves  of  sound  in  the  atmosphere, 
only  through  a  vastly  more  attenuated,  but  at  the 
same  time  more  elastic,  medium  which  he  called  the 
"  luminiferous  ether."  But  in  an  aeriform  medium, 
elasticity,  the  force  by  which  waves  are  transmitted, 
can  be  developed  only  by  compression.  Of  course 
compression  at  one  point  must  be  attended  by  expan- 
sion at  contiguous  points,  and  waves  of  sound  consist 
in  alternating  states  of  compression  and  expansion 
spreading  from  every  centre  of  disturbance.  Such 
alternating  conditions  must  produce  variations  of 
pressure  at  the  surfaces  which  the  medium  touches, 
and  the  phenomena  of  wave  motion  result  from  the 
concurrence  or  interference  of  such  partial  effects,  as 
Huygens  so  beautifully  showed. 
Although  the  general   order  of  the    appearances 


222  OBSERVATION   OF   MALUS. 

observed  in  the  double  refraction  of  light  by  Iceland 
spar  was  beautifully  explained  by  the  wave  theory  of 
Huygens,  yet  there  remained  certain  features  of  this 
striking  phenomenon  —  described  both  by  Huygens 
and  Newton — which  were  inexplicable  until  in  1810, 
when  Malus,  while  looking  through  a  double  refrac- 
ting prism  at  the  light  of  the  setting  sun  reflected 
from  the  windows  of  the  Luxembourg  Palace  at 
Paris,  first  observed  the  most  fundamental  of  that 
remarkable  series  of  phenomena  which  he  afterwards 
developed  and  referred  to  what  he  called  the  "  polar- 
ization of  light."  Malus,  who  was  a  disciple  of  the 
emission  theory,  ascribed  all  these  effects  to  a  po- 
larity in  the  light-bearing  corpuscles;  and  hence 
arose  a  name  which  is  meaningless,  and  indeed  con- 
fusing, on  the  basis  of  the  theory  of  undulations. 
As  soon,  however,  as  the  new  facts  came  to  be 
studied  in  the  light  of  the  undulatory  theory,  it  was 
seen  that  the  essential  feature  of  the  condition  which 
had  been  called  "polarization"  was  the  transmission  of 
the  luminous  energy  in  a  definite  plane;  and  that  the 
elementary  motions  in  that  plane  which  constituted 
the  wave  motion  must  take  place  at  right  angles  to 
the  direction  of  the  rays  of  light.  These  considera- 
tions led  to  a  profound  alteration  of  the  wave  theory, 
first  recognized  by  Thomas  Young,  but  afterwards 
worked  out  with  great  ability  by  Fresnel.  The  wave 
motion  could  no  longer  be  regarded  as  transmitted 
through  an  attenuated  gas  by  the  elasticity  of  com- 
pression, and  it  became  necessary  to  conceive  of  the 
ether  with  parts  held  in  definite  relative  positions,  as 
in  a  solid,  through  which  the  waves  are  transmitted 


ETHER   OF   SPACE.  223 

by  the  elasticity  of  tension.  In  a  word,  the  theory 
now  filled  space  with  an  attenuated  solid,  whose 
parts  are  bound  together  far  more  firmly  than  those 
of  steel. 

Consider  now  the  apparently  contradictory  quali- 
ties which  it  has  been  found  necessary  to  attribute  to 
the  ether  of  space,  in  order  to  explain  the  known 
phenomena  of  light  and  heat.  In  the  first  place,  as 
the  ether  does  not  give  rise  to  any  sensible  perturba- 
tions in  the  motions  of  the  heavenly  bodies,  we  must 
assume  that  it  has  no  perceptible  mass ;  so  that  a  solid 
block  of  ether  of  the  size  of  this  room  cannot  weigh 
more  than  a  fraction  of  a  grain.  But  while  having 
such  an  excessive  tenuity,  we  must  in  the  next  place 
assume  that  this  singular  solid  consists  of  parts 
bound  together  with  such  an  incredible  force  that, 
as  the  waves  in  passing  through  this  medium  tend  to 
part  or  force  together  the  ultimate  particles,  the  ac- 
tion and  reaction  over  each  inch  of  surface  must  be 
measured  by  millions  on  millions  of  pounds. 

Why  it  is  necessary  to  ascribe  such  an  incredible 
elasticity  to  the  luminiferous  ether  will  in  general  ap- 
pear from  two  considerations.  In  the  first  place  the 
immense  velocity  of  light  requires  this  great  elasti- 
city. Assuming  that  two  media  have  the  same  den- 
sity, their  elasticities  are  proportional  to  the  squares 
of  the  velocities  with  which  a  wave  travels  through 
them.  The  velocity  of  the  sound  wave  in  air  is  1100 
feet  a  second,  or  about  one  fifth  of  a  mile,  and  that  of 
the  light  wave  about  183,000  miles  a  second,  or 
nearly  one  million  times  faster;  so  that  in  proportion 
to  its  density  the  ether  must  have  an  elasticity  a  mil- 


224  TRANSMISSION   OF   POWER. 

lion  million  times  greater  than  air.  In  the  second 
place,  this  great  elasticity  is  required  in  order  to  trans- 
mit power  from  the  sun.  The  earth  is  but  one  of  a 
number  of  great  machines  which  are  run  by  the  sun. 
There  is  no  form  of  energy  manifested  on  the  earth 
which  cannot  be  traced  to  the  sun.  The  sun  is  the 
great  motor  from  which  all  this  power  comes,  just  as 
directly  as  the  power  which  runs  the  spindles  and 
looms  of  a  manufactory  is  transmitted  by  shafts,  pul- 
leys, and  belts,  from  a  turbine  wheel  in  the  basement. 
Now  these  connections  must  be  strong  in  proportion 
as  the  power  to  be  transmitted  is  great ;  and  so  the 
ether  which  transmits  the  power  from  the  sun  must 
be  strong  enough  to  do  the  work ;  and  if  you  reduce 
the  material  in  it  to  next  to  nothing  you  must  make 
what  is  left  proportionally  strong,  —  that  is,  ascribe  to 
it  this  immense  elasticity.  Of  course  the  imagination 
knows  no  bounds,  and  you  may  ascribe  to  the  ether 
any  extravagant  relations  you  please ;  just  as  you 
can  imagine  materials  so  strong  that  the  power  of 
Niagara  could  be  transmitted  with  shafts  no  larger 
than  wires,  and  belts  no  larger  than  horse-hairs. 
And  if  you  are  not  to  take  into  any  account  the  har- 
monies of  nature,  one  supposition  is  as  reasonable  as 
the  other. 

It  is  not,  therefore,  without  reason  that,  following 
the  authority  of  Jevons,  I  have  called  the  luminifer- 
ous  ether  an  adamantine  solid ;  and  yet  in  the  midst 
of  this  adamantine  mass  we  live  and  move  without 
perceiving  the  least  resistance.  In  general  two  ex- 
planations have  been  given  to  show  how  motion  in 
such  a  solid  medium  is  possible.     In  the  first  place,  it 


A  SEMI-LIQUID. 


--:> 


has  been  suggested  that  the  molecules  of  a  body 
may  pass  between  the  ultimate  particles  of  the  ether ; 
just  as  a  flock  of  birds,  regarded  as  constituting  one 
mass,  would  pass  between  the  branches  of  a  forest,  — 
the  body  not  displacing  the  ether  but,  as  it  were,  pene- 
trating it.  I  need  not  say  that  besides  the  difficulties 
of  conception,  there  are  insuperable  philosophical 
objections  to  this  view.  The  second  suggestion  is 
that  the  ether  is  a  semi-liquid,  which,  like  pitch  or 
ice  near  the  melting-point,  has  a  great  elasticity  as- 
sociated with  an  equally  great  degree  of  liquidity. 

Ice,  as  is  well  known,  flows  down-hill  in  the  glacier's 
streams;  and  so  will  pitch,  although  masses  of  either 
substance  have  marked  elasticity,  and  will  break  with 
a  conchoidal  fracture  like  glass.  Now  conceive  of 
the  ether  as  pouring  round  a  body,  passing  through 
it,  without  a  parting  of  the  ultimate  particles  of  the 
medium,  which  continue  to  cling  together  with  the 
immense  force  I  have  mentioned,  —  and  you  have 
the  most  recent  conception  that  has  been  advanced 
of  the  relations  of  this  inconceivable  material.  But 
obviously,  such  devices  of  the  imagination  do  not  in 
the  least  degree  remove  the  difficulty  of  the  concep- 
tion. Fundamentally,  this  difficulty  consists  in  asso- 
ciating great  extremes  of  qualities  which  from  our 
experience  seem  to  be  incompatible.  In  ice  or  pitch 
a  very  small  degree  of  liquidity  is  associated  with 
elasticity  of  tension ;  but  in  similar  semi-liquids  the 
elasticity  diminishes  in  proportion  as  the  liquidity  in- 
creases, while  in  the  ether  we  are  asked  to  associate 
indefinitely  great  elasticity  with  indefinitely  perfect 
liquidity. 


226  '     IRRECONCILABLE   RELATIONS. 

Such  utterly  incongruous  and  irreconcilable  rela- 
tions may  not  discredit  a  theory  as  a  system  of  sci- 
ence, but  they  must  shake  our  faith  in  its  credibility  as 
a  reality  of  nature.  As  we  have  already  said,  there  is 
nothing  in  science  so  improbable,  or  so  inconceivable, 
that  it  may  not  be  realized.  With  all  the  unknown 
relations  of  nature  it  is  not  safe  to  say  that  anything 
is  impossible,  unless  it  absolutely  conflicts  with  funda- 
mental laws.  We  are  doubtless  safe  in  expressing 
the  opinion  that  no  form  of  matter  or  energy  can  be 
produced  without  a  corresponding  expenditure ;  and 
that  those  who  stake  ventures  in  processes  for  making 
materials  or  obtaining  work  from  nothing  are  de- 
luded ;  but  much  further  than  this  it  is  not  safe  to 
prophesy.  It  is  within  our  own  experience  that 
steam  navigation,  ocean  telegraphy,  and  electrical 
lighting,  were  pronounced  impracticable  by  men  of 
large  knowledge  and  great  intelligence;  and  we  have 
lived  to  witness  their  confusion  in  the  accomplished 
results. 

In  all  such  cases,  however,  when  the  improbable 
has  been  once  realized,  it  has  been  found  to  be  in 
harmony  with  the  rest  of  our  knowledge;  and  it  has 
been  seen  that  the  seeming  incongruity  arose  from 
our  ignorance  of  general  principles,  or  other  links 
through  which  the  relationship  became  evident. 
Therefore,  while  repeated  experience  of  this  kind 
should  make  us  cautious,  it  cannot  but  increase  our 
confidence  in  the  general  trustworthiness  of  the  anal- 
ogies by  which  the  student  of  nature  is  so  greatly 
guided.  But  the  same  experience  should  also  make 
us  duly  sensible  of  the  limitations  of  our  knowledge, 


A   REAL   CORRESPONDENCE.  227 

and  inculcate  largeness  in  thought  and  reservation  in 
judgment. 

That  such  an  adamantine  medium  as  the  ether  of 
our  theories  actually  exists  I  cannot  for  a  moment 
believe ;  but  that  the  ether  is  our  crude  conception 
of  some  reality  which  bridges  the  celestial  spaces  I 
have  no  question.  Perhaps  in  time  the  fulness  of 
knowledge  will  come;  perhaps  it  is  incomprehensible 
to  our  limited  faculties ;  but  that  there  is  something 
corresponding  to  the  ether  of  our  imaginings,  I  feel 
as  confident  as  that  there  is  a  solid  crust  of  earth 
under  my  feet.  In  some  way  illimitable  power 
crosses  the  immense  gulfs  of  space ;  and  what  we 
catch  glimpses  of  in  the  darkness,  and  try  to  express 
in  our  material  symbols  —  whose  inadequacy  appears 
in  the  extravagances  of  our  theories  —  is  simply  an 
order  of  being  recognized  as  fully  in  the  infancy  of  our 
race  as  now ;  and  of  which  it  may  be  said  as  in  the 
days  of  Job :  "  Where  is  the  way  where  light  dwell- 
eth?  .  .  .  Knowest  thou  the  ordinances  of  heaven? 
Canst  thou  set  the  dominion  thereof  in  the  earth?" 

It  is  undoubtedly  in  consequence  of  the  large  ele- 
ment of  truth  which  the  great  systems  of  science 
contain,  in  spite  of  all  their  philosophical  absurdities 
and  formal  inconsistencies,  that  they  have  led  us  in 
several  cases  to  a  knowledge  of  magnitudes  which, 
although  entirely  beyond  our  powers  of  direct  obser- 
vation, have  been  measured  with  the  greatest  accuracy. 
In  the  undulatory  theory  this  is  true  in  regard  to 
the  lengths  of  the  waves  of  light;  and  although  there 
is  such  large  room  for  doubt  in  regard  to  the  nature 
of  these  magnitudes,  our  knowledge  of  their  values  is 


228  WAVES   OF  LIGHT. 

so  exact  that  it  has  been  seriously  proposed  to  use 
them  as  standards  of  linear  measurement.  Remember 
that  the  longest  of  the  luminous  waves  only  measure 
1-39,000  of  an  inch  —  counted  as  with  a  water-wave 
from  crest  to  crest  —  and  you  can  see  what  such  a 
proposition  implies,  and  also  what  must  be  the  order 
of  the  unknown  quantity  which  we  are  able  to  meas- 
ure so  accurately.  And  not  only  do  we  know  the 
values  of  those  magnitudes,  but  we  have  followed  out 
their  relations  through  most  intricate  conditions,  and 
found  our  deductions  most  completely  verified  at 
every  step  of  our  inquiry.  That  these  values  are 
the  magnitude  of  real  things,  we  can  have  no  more 
question  than  that  the  measurements  given  by  Piazzi 
Smyth,  in  his  work  on  the  Egyptian  Pyramids  are 
the  dimensions  of  actual  blocks  of  stone,  however 
much  archaeologists  may  question  this  learned  as- 
tronomer's theory  in  regard  to  the  purposes  for 
which  these  blocks  were  originally  wrought. 

But  besides  presenting  in  its  postulates  the  philo- 
sophical and  formal  incongruities  I  have  pointed  out, 
the  undulatory  theory  is  by  no  means  perfect  in  its 
appropriate  relations ;  for  there  is  a  most  important 
and  conspicuous  class  of  optical  facts  which  it  has 
as  yet  essentially  failed  to  explain.  I  refer  to  the 
beautiful  phenomena  on  which  spectrum  analysis  is 
based.  Newton's  earliest  experiment,  in  which  he 
separated  the  colored  rays  composing  white  light 
by  means  of  a  glass  prism,  still  challenges  the 
undulatory  theory.  I  have  already  referred  to  the 
remarkable  investigation  of  Cauchy  on  this  very 
point,  which  has  been  justly  regarded  as  a  monument 


THE   DISPERSION   OF   LIGHT.  229 


of  mathematical  skill ;  but  this  investigation  wholly 
failed  in  its  main  purpose.  The  most  that  Cauchy 
accomplished  with  his  profound  mathematical  anal- 
ysis was  to  show  that  such  effects  might  follow  from 
wave  motion  on  certain  assumptions  in  regard  to 
the  molecular  structure  of  the  dispersing  media;  so 
that  when  our  knowledge  of  molecular  structure  is 
more  complete,  the  undulatory  theory  may  possibly 
be  able  to  explain  the  phenomena  in  question.  He 
did  not  in  any  proper  sense  bring  the  phenomena  of 
dispersion  under  the  control  of  the  theory;  and  to 
the  average  student  they  remain  to  the  present  day 
as  inexplicable  as  ever.  If,  however,  Cauchy's  anal- 
ysis gives  us  good  reason  for  expecting  that  with 
larger  knowledge  we  may  be  able  to  include  the 
phenomena  of  dispersion  in  our  system,  there  are 
also  equally  strong  grounds  for  the  opinion  that 
before  this  can  be  done  the  present  undulatory 
theory  must  be  profoundly  modified. 

I  fear  that  in  thus  dwelling  on  the  inconsistencies 
and  imperfections  of  the  undulatory  theory,  it  may 
seem  as  if  I  were  aiming  to  discredit  the  system ; 
when  on  the  contrary  I  desire  to  exalt  it.  The  last 
word  has  always  such  undue  force  that,  to  avoid  mis- 
apprehension, it  is  almost  necessary  to  reiterate  the 
opinion  I  expressed  at  first,  — that  the  undulatory 
theory  of  light  is  one  of  the  noblest  creations  of 
science,  one  of  the  greatest  achievements  of  the 
human  intellect,  and  that  its  value  can  not  be  over- 
estimated. I  believe  that  the  system  is  no  more 
imperfect  than  is  necessarily  implied  in  saying  that 
it  is  a  product  of  human  thought,  that  it  involves 


230  THE   MOLECULAR  THEORY. 

human  conceptions,  and  must  necessarily  be  subject 
to  human  limitations.  My  aim  has  been  to  exhibit 
the  system  in  its  true  relations,  and  to  show  that  we 
must  be  content  to  use  it  for  what  it  is  worth,  and 
not  expect  to  reconcile  it  at  all  points  with  either 
our  speculative  opinions  or  our  limited  experience. 

We  come  now  to  the  third  of  the  three  great  sys- 
tems of  science  which  we  have  called  the  Molecular 
Theory,  and  this  presents  two  very  distinct  aspects, 
according  as  we  study  the  theory  from  a  physical 
or  from  a  chemical  standpoint.  On  certain  features, 
however,  both  the  physicists  and  the  chemists  agree. 
By  students  of  both  classes  the  mass  of  material 
bodies  is  regarded  not  as  uniformly  and  continuously 
distributed  through  the  spaces  they  seem  to  occupy, 
but  as  segregated  into  an  innumerable  number  of 
excessively  minute  masses  called  "  molecules,"  each 
of  which  is  a  separate  unit, —  as  much  so  as  a  planet. 

There  must  be  as  many  different  kinds  of  molecules 
as  there  are  distinct  substances,  but  all  the  molecules  of 
the  same  substance  —  as,  for  example,  the  molecules 
of  water  —  are  assumed  to  be  the  exact  counterparts 
of  every  other.  Of  the  absolute  size  of  the  molecules 
we  can  only  form  a  very  rude  estimate,  but  the  esti- 
mates made  in  different  ways  quite  closely  agree,  and 
a  conception  of  the  order  of  magnitudes  with  which 
our  theory  deals  is  best  given  by  means  of  the  illus- 
tration already  cited,  which  we  owe  to  Sir  William 
Thompson,  who  said  that  if  a  drop  of  water  were 
magnified  to  the  size  of  the  earth,  and  the  molecules 
of  water  magnified  in  the  same  proportion,  they 
would  certainly  appear  larger  than  "  marbles,"  and 


HEAT   A   MODE   OF   MOTION.  23 1 

smaller  than  cricket-balls.  Wonderfully  small  as 
these  magnitudes  must  be,  the  theory  does  not  on 
this  account  present  any  insuperable  difficulties  of 
conception ;  for  it  only  asks  us  to  believe  in  a  micro- 
cosmos  beneath  us,  in  some  measure  comparable 
with  the  macrocosmos  which  astronomy  has  shown 
to  exist  above  us.  The  difficulties  appear  when  we 
come  to  consider  the  attributes  and  relations  which 
our  theory  compels  us  to  ascribe  to  these  minute 
masses. 

In  physics  the  molecules  are  regarded  as  the 
points  of  application  of  forces  ;  as  for  example,  when 
a  body  is  expanded,  melted,  or  volatilized  by  heat. 
Indeed,  limiting  our  attention  in  this  direction  to 
thermal  phenomena,  heat  itself  is  regarded  as  mo- 
lecular motion,  and  it  is  an  established  fact  that  a 
given  quantity  of  heat  corresponds  to  a  definite 
amount  of  mechanical  work.  On  the  molecular 
theory,  quantity  of  heat  means  simply  quantity  of 
molecular  motion,  and  temperature  is  the  average 
moving  energy  of  individual  molecules.  Molecular 
and  mechanical  motion  are  interchangeable.  When 
a  cannon-ball  strikes  a  target  and  buries  itself  in  the 
iron  plate,  the  increased  temperature  of  the  united 
metallic  masses  is  the  result  of  the  transfer  of  the 
motion  of  the  ball,  as  a  whole,  to  the  molecules  of 
which  both  ball  and  target  consist ;  and  on  the  other 
hand,  the  piston  of  a  steam-engine  receives  all  its 
power  from  the  molecules  of  steam  which  rebound 
from  its  surface. 

Sir  William  Thompson  used  the  word  "  atoms," 
meaning  the  units  which  chemists  now  distinguish  by 
16 


232  THE  THEORY  RESTS   ON  ANALOGY. 

the  word  "molecules;"  but  both  atoms  and  mole- 
cules are  of  the  same  order  of  magnitude. 

Motion  is  thus  transferred  between  large  and  small 
masses  indifferently,  as  it  would  be  transferred  be- 
tween two  elastic  billiard-balls  ;  and  indeed  the  well- 
known  laws  of  collision  between  elastic  bodies  were 
the  basis  of  the  analogy  which  led  to  the  molecular 
theory.  But  in  transferring  our  conceptions  from 
ivory  balls  to  molecules  we  are  obliged  to  call  on  the 
imagination  to  take  one  of  those  extreme  flights 
which  all  similar  theories  demand.  Balls  of  ivory  or 
steel,  although  made  of  the  most  elastic  materials 
with  which  we  are  acquainted,  would  very  soon  come 
to  rest  in  knocking  about  among  each  other  ;  but  our 
molecules  must  be  so  perfectly  elastic  that  though 
each  one  makes  millions  of  collisions  every  second, 
yet  throughout  all  time  no  moving  power  is  lost. 

If  we  think  only  of  their  minuteness,  the  moving 
power  of  molecules  may  seem  insignificant;  but  the 
molecules  are  as  numerous  as  they  are  small,  and 
their  aggregate  moving  power  is  enormous.  When 
a  quart  of  water  is  heated  from  the  freezing  to  the 
boiling  point,  as  in  the  familiar  process  of  boiling  a 
teakettle,  an  amount  of  moving  power  is  imparted  to 
the  molecules  of  water  which,  if  transferred  to  a 
pound  cannon-ball,  would  impart  to  it  an  initial  ve- 
locity of  4,715  feet  a  second. 

In  a  solid  body  the  molecular  motions  are  limited 
by  the  various  forces  which  determine  its  structure, 
and  are  supposed  to  be  restricted  to  a  definite  orbit. 
In  a  liquid  the  motion  is  less  constrained,  but  is  lim- 
ited by  the  boundaries  of  the  liquid  mass.     In  a  gas, 


SUCCESS   OF  THE  THEORY.  233 

however,  the  molecular  motions  are  supposed  to  be 
entirely  free,  limited  only  by  mutual  collisions,  or  by 
the  walls  of  the  containing  vessel.  In  both  solids 
and  liquids  the  relations  are  both  so  complex  and 
obscure  that  the  molecular  theory  has  not  been  able 
to  solve,  except  to  a  very  limited  extent,  the  difficult 
problems  which  they  present;  but  with  aeriform 
matter  the  theory  has  been  far  more  successful,  and 
gives  a  very  satisfactory  explanation  of  most  of  the 
observed  phenomena.  The  tension  or  pressure  ex- 
erted by  a  gas  is  the  effect  of  molecular  bombard- 
ment; and  the  well-known  laws  of  Mariotte,  of  Charles, 
and  of  Avogadro,  which  define  the  condition  o(  aeri- 
form matter  have  been  shown  to  be  necessary  con- 
sequences of  the  molecular  theory. 

Like  the  modulatory  theory,  the  molecular  theory 
has  also  led  us  to  a  knowledge  of  magnitudes  which 
must  ever  evade  our  senses,  and  which  almost  defy 
our  imagination.  Thus  we  can  calculate  with  great 
accuracy  the  average  velocity  of  the  molecular  mo- 
tion in  any  gas  under  given  conditions,  —  that  in 
hydrogen  gas  at  the  freezing-point,  for  example,  being 
6,099  feet  m  a  second.  And  what  is  still  more  singu- 
lar, we  can  calculate  the  average  number  of  collisions 
per  second,  as  well  as  the  average  length  of  the  mo- 
lecular path  between  two  successive  collisions,  of 
course  under  definite  conditions.  In  hydrogen  gas, 
under  the  standard  conditions  of  temperature  and 
pressure,  each  molecule  strikes  against  its  fellows 
17,750  million  times  a  second;  and  the  average  mo- 
lecular path  is  only  3 1  ten-millionths  of  an  inch.  This 
last  seems  incredibly  small,  but   it   is   at   least  136 


234  DIFFICULTIES    OF   CONCEPTION. 

times  the  average  distance  between  two  molecules  ; 
and  in  an  assembly  of  men  such  an  allowance  would 
be  regarded  as  very  liberal. 

These  few  data,  which  might  be  greatly  multiplied, 
will  show  how  definite  are  the  conceptions  which  the 
molecular  theory  involves  ;  and  my  brief  description 
will  give  some  idea,  although  very  imperfect,  of  the 
scope  of  the  theory  itself.  I  can  only  add  that  in  its 
relations  to  aeriform  matter  the  theory  has  been  de- 
veloped mathematically  by  such  men  as  Rankine, 
Clausius,  and  Maxwell ;  and  that  it  gives  a  satisfac- 
tory account  of  the  efficiency  and  mode  of  action  of 
all  thermo-motors,  which,  like  the  steam-engine,  are 
such  important  factors  in  our  civilized  life. 

But  while  in  that  special  field  known  as  the  "  kin- 
etic theory  of  gases,"  the  molecular  theory  is  one  of 
the  best  elaborated  systems  of  modern  science,  it 
involves  difficulties  of  conception  fully  as  great  as 
those  we  met  in  connection  with  the  undulatory  the- 
ory of  light.  Not  only  must  we  ascribe  to  the  mole- 
cules a  perfection  of  attributes,  like  perfect  elasticity, 
which  we  only  find  in  material  bodies  to  a  very 
limited  degree,  but  also  we  must  associate  together 
attributes  which  from  our  experience  seem  to  be  in- 
compatible. We  must,  in  a  word,  give  up  all  our  or- 
dinary prepossessions,  and  accept  provisionally  what 
seem  to  us  monstrous  hypotheses  because  they  ex- 
plain facts  and  relations  which  would  be  otherwise 
isolated  phenomena,  and  because  they  are  parts  of  a 
system  which  as  a  whole  is  a  good  working  theory. 

Having  discussed  similar  difficulties  of  conception 
in  the  undulatory  theory  of  light,  it  is  unnecessary  for 


CHEMICAL   ASPECTS    OF  THE   THEORY.         235 


me  to  dwell  on  the  corresponding  features  in  the  sys- 
tem now  before  us.  They  obviously  result  from  the 
same  incompleteness  of  knowledge,  and  teach  the 
same  lessons  already  sufficiently  enforced.  Any  one, 
however,  who  desires  to  study  the  details,  will  find 
them  very  clearly  stated  by  J.  B.  Stallo,  in  his  admir- 
able book  on  "The  Concepts  and  Theories  of  Modern 
Physics,"  —  a  volume  of  the  International  Series  to 
which  I  take  great  pleasure  in  referring. 

I  wish  next  to  ask  your  attention  to  the  chemical 
side  of  the  molecular  theory ;  for  it  is  in  this  direc- 
tion that  it  has  run  into  the  greatest  extravagances ; 
and  yet,  singular  as  it  may  seem,  it  is  just  here  that 
it  has  proved  of  the  most  value  as  a  working  theory. 
In  addition  to  molecules,  the  chemist  is  obliged  to 
distinguish  a  still  smaller  subdivision  of  matter,  which 
he  calls  "  atoms."  The  ultimate  analysis  of  the  physi- 
cist goes  no  further  than  molecules;  but  the  ultimate 
analysis  of  the  chemist  breaks  up  the  molecules  and 
gives  us  atoms.  There  must  be  as  many  kinds  of 
molecules  as  there  are  distinct  substances ;  but  only 
as  many  kinds  of  atoms  as  there  are  elementary  sub- 
stances, some  seventy  at  most.  In  a  physical  change 
in  which  the  distinctions  of  substance  remain  unaltered 
the  integrity  of  the  molecules  is  preserved ;  but  in  a 
chemical  change,  which  necessarily  involves  a  change 
of  substance,  the  molecules  are  broken  up,  and  the 
atoms  regroup  themselves  to  form  the  molecules  of 
the  resulting  products. 

Thus  when  water  is  converted  into  steam,  the  mole- 
cules of  water  remain  unchanged,  and  are  only  driven 
more  widely  apart;   but  when  under  the  action  of  an 


236  THE   CHEMICAL  MOLECULE. 

electric  current  water  yields  oxygen  and  hydrogen 
gases,  the  molecules  of  water  are  broken  up  into 
atoms  of  oxygen  and  hydrogen,  which  regroup  them- 
selves to  form  the  molecules  of  these  aeriform 
products. 

In  fact  the  chemist  regards  the  molecule  in  quite 
a  different  light  from  the  physicist.  To  the  latter, 
molecules  are  chiefly  centres  of  force ;  while  to  the 
chemist  they  are  more  or  less  complex  structures  on 
which  depend  the  distinctions  and  relations  of  sub- 
stance. The  qualities  of  substances  are  all  referred 
to  the  molecules.  The  properties  which  distinguish 
water  from  alcohol,  or  sugar  from  salt,  depend,  not 
on  the  relations  of  any  perceptible  masses  of  these 
substances,  but  ultimately  on  the  constitution  of  their 
molecules.  Divide  up  a  lump  of  sugar,  and  you  may 
still  distinguish  the  qualities  of  sugar  in  the  smallest 
visible  particles ;  but  the  chemist  declares  such  a  sub- 
division could  not  be  carried  on  indefinitely,  even  if 
our  senses  could  follow  it.  We  should  soon  come  to 
the  smallest  possible  mass  of  sugar,  which  on  push- 
ing our  subdivision  further  would  break  up  into  atoms 
of  carbon,  hydrogen,  and  oxygen,  three  well-known 
chemical  elements.  This  smallest  possible  mass  of  a 
substance  is  the  chemist's  molecule;  and  hence  his 
definition,  —  "  the  smallest  mass  of  a  substance  which 
can  exist  by  itself." 

The  forces  which  bind  together  atoms  into  mole- 
cules we  distinguish  as  chemical  forces,  while  such 
as  determine  the  aggregation  of  molecules  to  form 
material  masses  are  said  to  be  physical,  although  we 
have  no  sufficient  reason  for  assuming  that  there  is 


DISSOCIATION.  237 


any  essential  difference  between  the  two ;  and  all  such 
forces,  whatever  may  be  their  nature,  are  overcome 
by  heat.  At  the  intensely  high  temperatures  which 
rule  at  the  sun  or  at  the  fixed  stars,  it  is  supposed 
that  the  elementary  atoms  are  isolated  and  intermin- 
gled, if  not  still  further  resolved ;  and  as  in  the  pro- 
cess of  evolution  of  our  system  the  planetary  masses 
have  cooled,  it  is  held  that  the  atoms  have  united  to 
form  the  molecules  of  various  substances,  and  that 
similar  molecules  have  then  aggregated  to  form  defi- 
nite material  products.  When,  now,  on  the  surface  of 
the  earth  we  heat  such  materials  to  the  highest  tem- 
peratures we  can  command,  the  process  of  world- 
building  is  to  a  limited  extent  reversed,  presenting 
us  with  a  remarkable  class  of  phenomena  known  as 
dissociation.  But  why  in  the  process  of  evolution 
unlike  atoms  should  unite  by  preference  to  form 
molecules,  while  in  the  further  aggregation  to  form 
material  products  only  like  molecules  should  asso- 
ciate together,  remains  an  unexplained  enigma. 

A  confusion  often  arises  from  the  use  of  the  word 
"  elementary"  in  connection  with  substances  as  well  as 
with  atoms.  The  atoms  are  the  only  true  chemical 
elements.  An  elementary  substance  like  oxygen  gas, 
sulphur,  or  iron,  is  an  aggregate  of  molecules  like 
any  other  substances,  and  externally  presents  no 
characters  by  which  it  can  be  recognized  as  elemen- 
tary. But  on  analysis  we  find  that  its  molecules  are 
formed  by  the  union  of  atoms  of  the  same  kind  only, 
while  the  molecules  of  compound  substances  consist 
of  atoms  of  different  kinds.  The  molecules  of  oxygen 
gas,  for  example,  are  aggregates  of  atoms,  as  well  as 


238  PHILOSOPHY   OF   CHEMISTRY. 

the  molecules  of  water ;  but  while  the  first  consist  of 
oxygen  atoms  only,  the  second  contain  atoms  of 
hydrogen  united  to  the  atoms  of  oxygen. 

Upon  the  distinction  between  atoms  and  molecules 
the  philosophy  of  modern  chemistry  rests,  and  its 
symbolical  language  is  based.  Each  one  of  the 
seventy  chemical  symbols  stands  for  an  atom.  By 
grouping  these  symbols  together,  like  letters  to  form 
a  word,  we  represent  the  infinite  possible  varieties  of 
molecules ;  and  then  all  chemical  changes  are  repre- 
sented by  an  equation,  writing  the  symbols  of  the 
substances  concurring  to  produce  the  change  in  the 
first  member,  and  the  symbols  of  the  substances 
resulting  from  the  change  in  the  second  member. 
Such  an  equation  declares  that  the  process  consists, 
as  already  said,  in  the  breaking  up  of  the  so-called 
factors  into  atoms,  and  the  regrouping  of  the  result- 
ing atoms  to  form  the  molecules  of  new  substances, 
the  products. 

In  the  vapor  of  mercury  immediately  above  the 
boiling-point,  the  atoms  appear  to  be  completely  dis- 
sociated, so  that  this  aeriform  substance  must  be  re- 
garded as  a  mass  of  isolated  atoms  ;  but  this  is  a  very 
exceptional  condition  on  the  surface  of  the  earth.  In 
a  few  of  the  elementary  gases  or  vapors,  and  in  some 
of  the  simpler  compounds,  we  are  able  to  recognize 
—  when  the  substances  are  aeriform  —  molecules  con- 
sisting of  only  two  or  three  atoms.  But  the  molecules 
of  most  bodies  are  far  more  complex;  and  although 
as  the  complexity  increases,  our  confidence  in  our 
inferences  diminishes,  yet  with  a  considerable  degree 
of  confidence  we  can  say  that  the  molecules  of  some 


MOLECULAR  STRUCTURE.  239 


of  the  most  familiar  materials  are  aggregates  of  more 
than  a  hundred  of  these  assumed  ultimate  elements 
of  matter. 

It  was  formerly  thought  that  the  qualities  and 
chemical  relations  of  a  substance  depended  on  the 
nature  of  the  elementary  atoms  of  which  its  molecules 
consisted,  and  resulted  from  a  blending  of  the  quali- 
ties of  the  chemical  elements  in  some  mysterious 
way ;  but  we  now  recognize  that  the  chemical  prop- 
erties of  substances  depend  in  great  measure,  at  least, 
on  the  manner  in  which  the  atoms  are  grouped  in 
their  molecules ;  and  the  order  in  which  the  different 
atoms  are  grouped  in  the  molecules  of  substances  is 
not  only  a  legitimate  object  of  inquiry,  but  is  a  sub- 
ject which  has  nearly  engrossed  the  attention  of  the 
chemists  of  the  world  for  the  past  twenty-five  years. 

It  would  be  impracticable  in  this  course  of  lectures 
to  give  any  clear  conception  of  the  nature  of  the 
evidence  on  which  our  knowledge  of  the  atomic 
structure  of  molecules  is  based,  or  of  the  course  of 
reasoning  by  which  the  accepted  conclusions  have 
been  established.  The  subject  is  abstruse,  and  could 
not  be  made  intelligible  without  entering  largely  into 
the  details  of  chemistry.1  In  any  modern  work  on 
organic  chemistry,  you  can  see  our  conceptions  of 
the  atomic  structures  of  the  molecules  of  various 
substances  exhibited  by  placing  the  atomic  symbols 
in  definite  relations  to  each  other  and  connecting 
them  by  dashes    supposed  to  represent  the  atomic 

1  I  have  endeavored  to  present  the  subject  in  a  popular  form 
in  my  "  New  Chemistry,"  and  to  that  book  I  must  refer  any  one 
who  desires  such  information. 


240 


STRUCTURAL   FORMULAE. 


bonds.  Such  graphic  representations  are  called  struc- 
tural formulae,  and  are  supposed  to  show  at  least  the 
order  in  which  the  several  atoms  are  united  in  the 
molecule.  A  single  example  of  a  structural  formula 
will  suffice  as  an  illustration :  — 


II 


H 


H 

H 

0 

C 

r,                \ 

C 

C 

xc           c 

0  c 

c 

c           c 
c 

\ 

o  c 
c 

c 
c 

H 

H 

O' 


H 


II 


Alizarine. 


To  one  who  realizes  what  is  thus  represented,  but 
who  is  not  familiar  with  the  evidence,  or  imbued 
with  the  spirit  of  the  matter,  it  must  seem  incredible 
that  these  apparently  fanciful  groupings  should  be 
sober  results  of  science;  and  yet  a  reason  can  be 
given  for  the  position  of  every  symbol  and  of  every 
dash,  which  —  if  the  postulates  are  granted  —  must 
be  admitted  to  be  cogent.  Moreover  —  what  is  the 
more  remarkable  fact  —  by  following  out  the  indica- 
tions of  such  structural  formulae  chemists  have  suc- 
ceeded in  preparing  artificially  a  very  large  number 
of  exceedingly  complex  compounds  whose  produc- 
tion under  such  circumstances  could  not  but  inspire 
the  greatest  confidence  in  the  general  correctness 
of  the  reasoning  on  which  the  structural  formulae 
were  based.     Some  of  these  products,  like  alizarine, 


CONVENTIONAL   SYMBOLS.  24I 

the  coloring- matter  of  madder-root,  —  now  prepared 
artificially  from  anthracene,  one  of  the  constitu- 
ents of  coal  tar,  —  have  such  great  commercial  im- 
portance that  these  theoretical  investigations  have 
completely  revolutionized  large  branches  of  human 
industry.  Indeed  if  certainty  of  prediction  is  to  be 
regarded  as  the  test  of  validity,  there  is  not  one  of 
the  great  systems  of  science,  excepting  the  the- 
ory of  gravitation,  which  has  so  completely  vindi- 
cated its  legitimacy  as  has  this  molecular  theory  of 
chemistry. 

But  although  our  structural  formulae  have  this 
wonderful  power  of  prediction,  and  are  therefore  of 
the  highest  value  as  a  system  of  science,  yet  no 
philosophical  chemist  thinks  of  regarding  them  as 
more  than  conventional  symbols  of  relations  which 
are  at  present  incomprehensible.  I  would  urge  this 
point  with  special  emphasis;  because,  although  the 
same  feature  appears,  as  I  have  shown,  in  connection 
both  with  the  theory  of  gravitation  and  with  the  un- 
dulatory  theory  of  light,  it  has  been  said  that  the 
difficulties  of  conception,  which  an  inherent  gravitat- 
ing force  or  an  adamantine  ether  present  are  of  no 
weight  in  view  of  the  so  general  accordance  of  these 
theories  with  observed  facts.  In  the  present  case  no 
such  claim  can  for  a  moment  be  maintained.  All  the 
conceptions  are  'obviously  conventional ;  and  yet  we 
have  the  same  wonderful  gift  of  prophecy.  Is  not 
the  lesson  plain?  Man  must  work  under  limitations; 
he  must  often  be  content  with  the  shadow  instead  of 
the  substance  of  realities;  but  he  may  with  confi- 
dence follow  his  earth-born  systems  of  philosophy,  if 


242    THEORY  OF  ORGANIC  DEVELOPMENT. 

only  they  are    grounded  on    experience  and    estab- 
lished in  loyalty  to  truth. 

And  if  this  course  of  conduct  be  safe  and  legiti- 
mate in  one  realm  of  thought  it  certainly  must  be 
equally  so  in  every  other.  Spiritual  experience  can 
be  no  exception  to  the  general  principle. 

"  Finding,  following,  keeping,  struggling, 
Is  He  sure  to  bless  ? 
Saints,  apostles,  prophets,  martyrs 
Answer,  '  Yes.'  " 

Of  the  four  great  dominant  systems  in  modern 
science  to  which  I  referred  at  the  opening  of  this 
lecture  I  have  as  yet  spoken  of  but  three.  The  fourth 
during  the  last  twenty-five  years  has  attracted  more 
attention  than  all  the  rest  combined,  and  is  insepara- 
bly associated  with  the  name  of  that  chief  of  natural- 
ists, Charles  Darwin.  All  these  systems  have  been  in 
their  turn  the  subject  of  controversy;  and  too  often 
the  introduction  of  irrelevant  theological  issues  has 
added  acrimony  to  the  debate.  I  say  irrelevant  be- 
cause, if  the  position  I  have  taken  in  regard  to  the 
relations  of  scientific  systems  to  actual  knowledge  be 
correct,  there  can  be  no  real  issue  between  theology 
and  the  theories  of  science,  —  any  more  than  between 
theology  and  the  theory  of  music.  In  my  view  of 
the  subject  it  is  as  useless  to  seek  for  theological  an- 
tagonism in  Darwinism  as  it  would  be  to  look  for  it 
in  the  Calculus. 

In  regard  to  the  other  systems,  whatever  differ- 
ences of  opinion  may  remain,  all  feeling  about  the 
matter  has  long  since  disappeared ;  but  in  regard  to 
Darwinism,  while  the  blaze  of  theological  protest  with 


POSTULATES   OF   DARWINISM.  243 

which  the  theory  was  first  received  has  died  down, 
the  embers  of  the  excitement  still  remain;  and  it  is 
more  difficult  to  discuss  the  subject  dispassionately. 
In  another  place  I  have  before  strongly  urged  the 
irrelevancy  of  theological  issues  on  this  question; 
and  I  will  only  add  here  a  few  remarks,  which  may 
be  deemed  pertinent  because  showing  how  the  subject 
is  viewed  by  a  student  familiar  with  the  bearings  and 
use  of  theories  in  a  very  different  department  of 
science.  Further  than  this  I  do  not  feel  that  it  is 
within  my  province  to  discuss  the  subject;  for  my 
special  studies  have  been  limited  to  a  very  different 
field ;  and  I  have  not  that  detailed  knowledge  which 
alone  would  entitle  me  to  express  an  authoritative 
opinion  on  the  merits  of  the  system. 

The  theory  of  Darwin  rests  on  three  distinct  postu- 
lates. The  first  is  that  the  existing  species  of  plants 
and  animals  are  not  independent  creations,  but  the 
results  of  a  gradual  evolution  from  earlier  forms. 
The  second  is  that  while  in  the  provisions  of  nature 
for  the  propagation  of  all  living  beings  there  is  evi- 
dently a  strong  striving  for  the  conservation  of  types, 
there  is  also  a  manifest  tendency  to  variation,  which 
although  barely  perceptible  in  single  steps  may  go 
on  increasing  in  successive  generations  to  an  unlim- 
ited extent.  The  third  is  that  in  the  struggle  for 
existence  those  variations  are  preserved  which  are 
best  adapted  to  the  environment,  and  which  therefore 
protect  the  individuals  possessing  them  in  the  midst 
of  the  terrible  mortality  which  the  struggle  for  exist- 
ence entails. 

However   many  facts    or   considerations   may   be 


244  ANTIQUITY   OF   MAN. 


urged  in  their  support,  there  is  not  one  of  these 
propositions  which  has  been  demonstrated  beyond 
reasonable  doubt ;  so  that  this  theory,  like  the  other 
great  theories  of  science,  rests  on  hypotheses,  and 
must  be  judged  as  a  scientific  system  by  the  com- 
pleteness with  which  it  explains  the  phenomena  of 
nature. 

In  regard  to  the  first  proposition  it  seems  strange 
that  with  all  the  attention  which  has  been  directed  to 
the  point  during  the  last  twenty-five  years  the  fact  of 
a  transition  between  two  well-marked  species  has  not 
yet  been  established  conclusively.  For,  admitting 
all  that  has  been  said  in  regard  to  the  slowness  of 
the  transition,  or  the  imperfection  of  the  geological 
record,  yet  considering  the  extent  of  the  field  that 
has  been  surveyed,  it  seems  very  strange  that  more 
of  the  missing  links  have  not  been  found.  We  can 
point  with  great  precision  to  definite  geological  hori- 
zons—  to  use  a  now  familiar  technical  term  —  on 
which  certain  species  of  well-marked  types  appeared 
on  earth;  and  certainly,  on  the  hypothesis  we  are 
considering,  it  is  strange  that  we  can  in  no  case  point 
unhesitatingly  to  other  species  in  lower  strata  from 
which  they  descended,  on  the  evidence  of  an  un- 
broken series  of  the  intermediate  forms  between 
the  two. 

Take  the  case  in  which  we  are  the  most  interested, 
that  of  our  own  race.  Assume  all  that  is  claimed 
in  regard  to  the  antiquity  of  man.  Still,  there  is  a 
definite  horizon  of  the  tertiary  epoch  below  which 
man  is  not,  but  above  which  his  remains  are  found 
in   ever  increasing  abundance,  with  all  the  features 


GROWTH   THE   ORDER   OF  NATURE.  245 


of  man  and  his  works  as  strongly  marked  as  they 
are  to-day.  Skeletons  of  these  primeval  men,  and 
their  belongings,  are  to  be  seen  in  our  ethnological 
museums;  and  there  are  no  greater  differences  of 
structure  between  them  and  ourselves  than  between 
the  different  races  which  inhabit  the  earth  at  the 
present  day.  But  if  man  be  descended  from  "an 
anthropoid  animal  of  arboreal  habits,"  it  is  passing 
strange  that  so  far  as  any  direct  evidence  goes,  he 
should  have  appeared  on  the  earth  thus  suddenly, 
and  that  we  can  find  no  traces  of  his  progenitors 
either  of  the  first,  second,  third,  or  of  any  other 
generation. 

Nevertheless,  the  hypothesis  of  a  gradual  genesis 
of  organic  types  seems  to  me  not  only  reasonable 
in  itself,  but  also  in  harmony  with  what  we  know  of 
nature's  workings.  Growth,  and  not  spasmodic  ef- 
fort, is  the  usual  order  of  the  divine  government 
both  in  the  material  and  in  the  spiritual  world ;  and, 
reasoning  from  analogy,  it  is  the  method  by  which 
we  should  expect  a  new  race  of  plants  or  animals 
would  be  introduced  into  the  world.  Indeed,  from  a 
scientific  point  of  view  any  other  mode  is  wholly  un- 
thinkable. Conceive  of  an  elephant  suddenly  appear- 
ing in  a  tropical  jungle,  like  a  jack  in  a  box,  without 
any  antecedents  except  a  fiat;  and  see  if  the  thought 
does  not  put  to  confusion  every  dictate  of  your  expe- 
rience, and  every  principle  of  your  intelligence.  You 
will  then  clearly  see  that  if  by  mortifying  reason  the 
doctrine  of  independent  creations  can  be  accepted 
as  a  wonder,  it  cannot  possibly  be  reconciled  with 
the   rest  of  your   knowledge.      Attempt   further   to 


246  QUESTION   OF   INTERPRETATION. 

realize  in  imagination  the  genesis  of  the  first  man. 
Was  he  suddenly  created  in  his  full  development 
and  strength,  prepared  to  subdue  nature?  or  did  he 
come  into  the  world  as  an  infant,  as  have  come 
all  of  his  race  since,  —  even  the  Saviour  of  the 
world? 

Do  not  deem  such  questions  irreverent.  They  are 
asked  in  that  spirit  of  truth  and  soberness  which 
sanctifies  any  inquiry.  They  ought  not  to  be  further 
pushed  in  this  place ;  but  the  suggestions  they  make, 
if  followed  out  in  your  own  reflections,  will  bring  you 
to  the  point  of  view  from  which  a  naturalist  is  com- 
pelled to  look  at  the  question  of  the  origin  of  spe- 
cies. Roman  mythology  provided  the  heaven-born 
founders  of  their  state  with  a  foster-mother;  and  it 
is  a  similar  necessity  of  thought  which  has  led  to 
what  is  usually  regarded  as  the  most  objectionable 
feature  of  Darwinism.  And  apart  from  the  au- 
thority of  any  undoubted  declaration  to  the  con- 
trary, why  should  we  be  shocked  by  the  hypothesis 
here  involved? 

On  the  other  hand,  it  may  be  said,  You  admit  that 
any  prodigy  must  be  accepted  in  science  on  ade- 
quate evidence ;  why  not  then  receive  the  plain  doc- 
trine of  independent  creations  taught  by  the  Hebrew 
Scriptures?  To  this  the  Christian  naturalist  replies 
that  all  such  inferences  from  the  Scriptures  must  be 
to  a  very  great  extent  questions  of  interpretation; 
and  that  in  this  case,  as  in  so  many  instances  before, 
the  interpretation  will  be  reconciled  with  the  facts  as 
soon  as  the  truth  plainly  appears.  And  in  the  sec- 
ond place,  he  will  add  that  while  in  science  no  won- 


POSSIBILITY   OF   INTERFERENCE.  247 


der  is  so  great  that  it  may  not  be  realized,  so  also 
no  marvel  is  so  sacred  that  it  may  not  be  reverently 
investigated ;  and  that,  whatever  the  event,  the  show- 
ing forth  of  the  truth  can  only  redound  to  the  glory 
of  God.  Again,  he  may  urge  that  this  is  a  question 
between  the  interpretation  of  Nature  on  one  side  and 
of  Scripture  on  the  other,  and  that  it  ought  not  to 
be  prejudged  by  assuming  the  infallibility  of  our  ren- 
dering .of  either  of  these  two  co-ordinate  authorities. 

Moreover,  this  is  not  a  question  of  creative  power 
nor  of  Divine  Providence.    After  all  has  been  granted 
that  any  one  can  claim  in  regard  to  the  constancy  of 
the  laws  which  we  fully  understand,  there  is,  as  has 
been  plainly  shown,  abundant  room  left  for  interfer- 
ence; and  it  is  more  consistent  with  our  conceptions 
of  the  Divine  method  to  suppose  that  God  works  by 
introducing  new  conditions  into  old  chains  of  causa- 
tion than  by  spasmodic  acts  of  creation,  which  must 
inevitably   confuse   and    confound    the    intelligences 
he  holds  so  dear.     That  such  interference  has  taken 
place,  it  seems  to  me  that  the  transition  from  a  geo- 
logical to  an  archaeological  museum  as  plainly  shows 
as  any  record   can  whose  meaning  has  been  left  to 
human  interpretation.     And  when  with  every  Yule- 
tide  the    Christ   Child  becomes  the  emblem   of  all 
that  is   lovely,   pure,   and  holy,  why  should  we  be 
alarmed    at   the    supposition    that   as    the    Child    of 
Mary  "grew  and  waxed  strong  in  spirit"  so  in  the 
beauty  of  innocence,  human  intelligence  at  first  slowly 
awakened  to  the  wonders  of  this  earth  ? 

In  regard  to  the  second  postulate  on  which  Dar- 
winism rests,  we  must  admit  that  this  also  is  to  a  great 
17 


248  EVIDENCE   INCONCLUSIVE. 

extent  in  harmony  with  well-established  facts.  No 
one  can  study  the  aspects  and  characters  of  a  family 
of  children  without  being  struck  with  the  undoubted 
truth  that  while  minute  details  of  features  both  of 
body  and  mind  are  wonderfully  preserved,  striking 
variations  from  the  parent  type  are  equally  conspic- 
uous. The  same  is  seen  to  be  even  more  markedly 
true  of  the  lower  animals  when  we  watch  them  as 
closely ;  and  when  we  think  of  it,  the  wonder  is  that 
the  variations  are  not  greater  than  they  are. 

There  is  nothing  in  our  actual  knowledge  of  na- 
ture which  makes  it  any  less  strange  that  an  acorn 
should  always  grow  into  an  oak  than  that  a  race 
of  monkeys  after  unnumbered  generations  should 
assimilate  to  men ;  and  we  know  of  no  reason  what- 
ever why,  with  an  equal  experience,  one  change 
should  not  appear  as  natural  as  the  other.  Indeed 
I  feel  confident  that,  with  all  our  knowledge  of  em- 
bryology, any  one  who  reflects  on  the  mysteries 
which  the  beginnings  of  life  both  in  plants  and  ani- 
mals present,  will  conclude  that  it  is  a  far  more  re- 
markable fact  that  every  creature  should  produce  of 
its  kind,  than  that  occasional  variations  should  occur. 
Nor  is  there  any  reason  why  we  should  be  surprised 
to  learn  that  in  successive  generations  the  variations 
should  become  cumulative,  and  lead  to  such  a  de- 
parture from  the  original  type  as  to  amount  to  a 
difference  of  species. 

As  before  said,  however,  it  is  strange  that  the 
evidence  of  such  a  transition  is  so  limited  and  incon- 
clusive ;  and  moreover,  as  was  so  strongly  urged  by 
the  late  Professor  Agassiz,  that  the  variations  pro- 


NATURAL   SELECTION.  249 

duced  by  domestication  —  which  have  been  so  care- 
fully studied  by  the  propagators  of  plants,  and  the 
breeders  of  stock — all  tend  to  revert  to  the  original 
wild  condition. 

Coming  lastly  to  the  third  postulate,  we  find  in  this 
also  a  general  principle  which  appears  to  a  student 
of  nature  highly  plausible.  The  struggle  for  life 
among  the  lower  animals  is  a  condition,  the  violence 
and  destructiveness  of  which  is  wholly  unappreciated 
except  by  those  who  have  made  a  special  study  of 
the  subject.  The  survivors  of  this  internecine  war- 
fare who  finish  their  allotted  span  of  life  are  fre- 
quently not  one  in  a  hundred,  often  not  one  in  a 
thousand.  Tennyson  quite  understates  the  condition 
when  he  speaks  of — 

"  finding  that  of  fifty  seeds 
She  often  brings  but  one  to  bear." 

Even  in  our  own  race  the  mortality  is  frightful  to  con- 
template, —  as  Malthus  has  so  vividly  depicted  it  in 
his  great  work  on  population.  Professor  Wallace,  who, 
independently  of  Darwin,  and  almost  at  the  same 
time,  originated  the  doctrine  of  natural  selection,  has 
distinctly  said  that  it  was  the  work  of  Malthus  which 
gave  him  the  key  to  the  problem;  and  it  is  well 
known  that  Darwin  himself  was  also  strongly  influ- 
enced by  the  facts  so  powerfully  set  forth  in  that  re- 
markable book.  I  only  repeat  what  some  of  you  must 
have  heard  from  Professor  Wallace's  own  lips  when 
I  say  that  until  one  realizes  the  prodigal  destruc- 
tiveness of  nature  it  is  impossible  to  appreciate  the 
strength  of  the  doctrine  of  natural  selection.  Wallace 
also  has  stated  that  the  generalization  came  to  him  as 


2  50  ADAPTATION   TO   THE   ENVIRONMENT. 

a  sudden  thought,  —  when,  overpowered  with  what 
he  was  constantly  witnessing  in  the  East  Indies,  he 
stopped  to  reflect  on  the  necessary  issues  of  such 
fearful  mortality.  The  "survival  of  the  fittest"  was  to 
him  a  fact  of  observation;  and  by  the  indiscriminate 
slaughter  of  all  others,  a  selection  was  seen  to  be 
made  of  those  creatures  whose  features  best  fitted 
them  to  cope  with  their  surroundings.  The  conclu- 
sion was  that  any  accidental  variation  in  color  or 
form  which  better  equipped  the  animal  for  the  in- 
evitable fight  must  be  preserved ;  and  that  thus  came 
the  gradual  adaptation  to  the  environment  in  which 
natural  selection  consists. 

All  this  is  plausible,  and  to  most  naturalists  con- 
clusive ;  and  that  the  struggle  for  existence  must 
tend  to  perpetuate  varieties  seems  to  be  beyond 
question.  It  still  remains,  however,  to  determine 
how  far  variations  thus  caused  can  proceed ;  and 
whether  they  can  ever  lead  to  fundamental  differ- 
ences of  type.  The  assumption  that  all  forms  of 
plants  and  animals  may  have  been  thus  produced 
from  a  few  germs  is  as  yet  an  hypothesis,  to  be 
judged,  like  any  other  hypothesis,  by  the  extent  to 
which  it  explains  and  correlates  facts.  Let  it  not  be 
prejudged  on  any  theory  of  Divine  government,  or 
on  the  basis  of  any  speculative  views  about  the  na- 
ture of  causation  ;  for,  were  the  hypothesis  estab- 
lished without  reservation,  —  a  most  improbable  event, 
judging  from  the  past  history  of  science,  —  the  new 
truth  would  only  serve  to  enlarge  our  views  of  the 
mode  of  the  Divine  government ;  and  there  is  abun- 
dant room  for  causation  left. 


VALUE   OF  THE   THEORY.  25  I 

Assume  that  the  variations  preserved  by  natural 
selection  are  all  accidental,  a  point  on  which  natu- 
ralists greatly  differ,  still  what  is  the  result?  An 
adaptation  to  the  environment.  According  to  the 
theory,  then,  the  conditions  of  the  environment  are 
a  determining  cause ;  and  unless  we  believe  that  all 
nature  was  the  result  of  a  fortuitous  concourse  of 
atoms,  we  can  find  in  these  conditions  abundant 
opportunities  where  intelligent  causation  can  act. 
And  the  thought  which  the  terrible  facts  implied  in 
our  theory  force  on  the  mind,  are  they  not  wholly  in 
harmony  with  what  we  believe  in  regard  to  the  Di- 
vine plan?  Everywhere  in  this  world  are  not  benefi- 
cent results  worked  out  through  suffering?  And  to 
the  lines  of  the  English  poet  which  I  have  just 
quoted,  must  I  not  add  the  anti-strophe  from  pre- 
ceding stanzas?  — 

"  O  yet  we  trust,  that  somehow  good 
Will  be  the  final  goal  of  ill, 
To  pangs  of  nature,  sins  of  will, 
Defects  of  doubt  and  taints  of  blood. 

"  That  nothing  walks  with  aimless  feet, 
That  not  one  life  shall  be  destroyed, 
Or  cast  as  rubbishto  the  void, 
When  God  hath  made  the  pile  complete." 

Finally,  looking  at  the  Darwinian  theory  of  devel- 
opment for  a  few  moments  as  a  whole,  I  would  re- 
mark that  it  has  not  the  completeness  of  the  other 
dominant  theories  of  science;  and  that  the  modes  of 
action  which  it  predicates  have  not  been  worked  out. 
It  is  a  doctrine  rather  than  a  complete  system  of 
science.     Nevertheless,  it  is  a  doctrine  which  exerts 


252  ORGANIC   TYPES. 


very  great  power.  It  owes  its  influence  over  natural 
history  students  solely  to  the  wonderful  effect  it  has 
exerted  in  directing  and  stimulating  investigation,  as 
well  as  to  its  capability  of  exhibiting  order  and  har- 
mony among  many  classes  of  facts  whose  relations 
before  were  very  obscure,  if  not  wholly  unrecogniz- 
able. Its  influence  on  the  religious  thought  of  the 
student  will  depend  very  greatly  on  the  manner  in 
which  its  philosophy  is  presented  by  his  religious 
teachers ;  and  I  therefore  greatly  deprecate  hasty 
judgment  or  indiscriminating  censure.  Remember 
that,  though  not  proven,  it  is  a  useful  and  admirable 
theory  of  science,  and  can  be  made  an  influence  for 
good  instead  of  for  evil,  if  only  set  forth  in  the  right 
light,  and  candidly  accepted  for  its  great  worth 
within  its  proper  sphere  and  just  limitations.  Set 
at  naught  all  questions  of  intelligent  or  unintelligent 
causation  as  irrelevant,  on  which  scientific  theories 
have  no  bearing.  The  character  of  the  First  Cause 
cannot  be  judged  from  the  mode  of  action  of  any 
secondary  agencies.  One  mode  of  action  is  as  mys- 
terious as  another,  so  far  as  any  relations  to  a  First 
Cause  are  concerned.  The  intelligence  of  the  First 
Cause  can  only  be  judged  from  the  result.  Each 
man  has  grown  from  a  germ ;  and  we  do  not  disown 
creative  power  when,  for  the  sake  of  a  consistent 
system,  we  assume  that  the  species  grew  as  well. 

I  myself  deprecate  the  present  domination  of  the 
Darwinian  theory,  not  on  account  of  what  it  is  in 
itself,  but  because  it  has  for  a  time  thrust  to  one  side, 
and  cast  into  the  shade,  the  doctrine  of  "  organic 
types  "  so  ably  and  so  forcibly  advocated  by  my  late 


ORGANIC   TYPES.  253 


teacher  and  colleague,  Professor  Louis  Agassiz,  and 
which  I  believe  to  be  the  more  valuable  system  of 
the  two,  at  least  in  one  important  respect. 

The  conception  that  each  of  the  four  great  fam- 
ilies of  the  animal  kingdom  is  a  definite  plan,  a  spe- 
cific design,  a  creative  thought,  worked  out  in  infinite 
variety,  and  adapted,  possibly  through  the  principles 
of  natural  selection,  to  varying  conditions  of  soil  or 
climate,  is  to  me  a  far  grander  and  more  compre- 
hensive doctrine  than  the  one  which  now  so  exclu- 
sively prevails.  The  idea  that  types  of  structure  are 
forms  of  thought  is  moreover  an  hypothesis  which 
has  very  great  intellectual  reach  and  educational 
value ;  and  for  this  great  virtue  of  the  older  theory, 
Darwinism  offers  no  sufficient  substitute.  When  now 
we  consider  that  the  educational  power  of  a  scientific 
system  is  its  chief  element  of  strength,  we  cannot  but 
regret  that  the  present  generation  will  lose  much  of 
the  charm  which  the  grand  conceptions  of  Cuvier  and 
Agassiz  imparted  to  the  study  of  natural  history. 

It  is  to  be  expected  that  a  theory  at  once  so  origi- 
nal and  so  fruitful  of  suggestions  as  Darwinism 
should  for  a  season  control  thought,  and  engross 
attention.  But  time  may  be  trusted  to  place  all 
human  systems  in  their  true  relations;  and  I  feel 
confident  that  the  doctrine  of  organic  types  will 
before  long  exert  its  just  influence.  The  new  and 
the  older  conceptions  are  not  mutually  exclusive. 
Whatever  is  true  in  each  will  survive;  whatever  is 
false  will  be  forgotten;  and  out  of  the  limited  hy- 
potheses of  to-day  will  grow  the  larger  views  of 
coming  generations. 


254  THE   DOGMATIST. 


Having  discussed  the  more  characteristic  features 
of  the  dominant  systems  of  science,  I  will  next  add  a 
few  words  in  regard  to  the  attitude  of  scientific  schol- 
ars towards  these  systems,  as  there  are  marked  differ- 
ences in  this  respect  which  strikingly  illustrate  a 
point  I  desire  to  emphasize. 

In  the  first  place,  then,  we  distinguish  a  very  large 
and  efficient  class  of  scientific  scholars  who  are  wholly 
wedded  to  the  system  of  science  by  which  their  stud- 
ies are  directed.  They  are  men  to  whom  the  system 
gives  strength  and  motive,  and  their  whole  intellectual 
life  has  been  moulded  by  their  guide.  No  wonder 
that  they  value  the  system,  for  it  has  made  them  what 
they  are,  and  without  it  they  would  be  to  a  great 
extent  helpless.  They  are  not  men  who  originate 
systems  or  strike  out  new  paths  of  discovery,  but 
they  are  men  who  with  a  well-defined  aim  work  zeal- 
ously and  efficiently.  The  system  has  opened  to 
them  new  fields  of  investigation  from  which  they 
have  reaped  an  abundant  harvest.  They  have  thus 
extended  the  boundaries  of  knowledge,  and  are  in 
consequence  deservedly  highly  honored  by  their  fel- 
low-men. It  is  impossible  that  a  system  through 
which  they  have  realized  such  great  results,  should 
be  at  fault  or  even  have  a  blemish.  Imperfections, 
which  to  other  men  appear  glaring,  they  refer  to 
errors  of  observation  ;  inconsistencies  are  overlooked 
or  ingeniously  explained  away,  and  mere  philosophi- 
cal objections  are  laughed  to  scorn.  By  such  men 
the  obvious  symbolism  of  the  system  often  comes  to 
be  regarded  as  a  likeness  of  real  things ;  and  they 
dwell  with  equal  emphasis  on  the  essentials  and  the 


THE   DOGMATIST.  255 


non-essentials  of  these  arbitrary  signs.  Sometimes 
they  even  parade  the  extravagances  of  the  system  in 
order  to  testify  more  conspicuously  their  allegiance 
to  their  leader. 

Such  men  are  apt  to  be  dogmatic,  and  to  demand 
conformity  to  their  well-grounded  opinion  as  well  as 
deference  to  their  long  experience.  They  do  not 
readily  brook  dissent,  especially  from  younger  men ; 
and  when  they  have  the  power,  they  are  sometimes 
tyrannical.  The  tyranny  of  a  system  is  often  as  cruel 
as  the  tyranny  of  a  despot,  and  may  be  exercised 
with  complacency  and  self-respect  by  the  "  mens  sibi 
conscia  recti,"  who  thinks  he  holds  the  keys  of  knowl- 
edge. We  must  not  overlook  what  is  often  noble 
and  worthy  in  these  men.  They  are  actuated  by  the 
power  of  conviction  which  a  successful  system  in- 
spires, and  the  intolerance  of  conviction  is  often  asso- 
ciated with  all  that  is  pure,  lovely,  and  of  good  report. 
There  is  a  still  nobler  charity,  which  never  faileth ; 
but  scholars  are  not  always  saints,  and  ostracism  is 
a  form  of  persecution  which  requires  no  sanguinary 
edicts.  The  noblest  martyrs  of  science  are  not  those 
who  have  braved  great  dangers  and  succumbed  only 
before  the  unattainable;  but  rather  those  who  have 
suffered  even  unto  death,  in  consequence  of  deprecia- 
tion, deprivation,  and  neglect.  I  have  known  of  such, 
and  among  them  the  founders  of  one  of  the  now 
dominant  systems  of  science.  Boycotting  did  not 
originate  in  Ireland ;  and  among  men  of  learning 
supercilious  sneers  may  cause  more  suffering  than 
blackballing.  Scientific  societies  are  probably  no 
worse  than  other  associations  of  men ;  but  they  have 


256  THE  THEORIST. 


often  been  subservient  to  the  intolerance  of  doctrine, 
and  the  domination  of  system. 

A  very  much  smaller  class  of  scientific  scholars 
display  a  habit  of  mind  the  very  reverse  of  that  I 
have  just  described.  These  men  are  superior  to 
systems,  of  which,  however,  they  speak  with  respect 
and  condescension  as  the  necessities  of  weak  minds. 
They  boast  of  their  freedom  from  prejudice,  and  of 
their  eclecticism  in  thought.  They  magnify  incon- 
sistencies of  doctrine,  or  incompleteness  of  evidence. 
They  expose  the  extravagances  of  the  assumptions, 
or  the  unsoundness  of  the  philosophy  on  which  the 
dominant  system  is  based.  They  are  apt  to  be  severe 
critics,  and  not  to  make  due  allowance  for  the  limita- 
tions of  methods  or  the  necessary  imperfections  of 
all  material  results.  They  deal  with  negations  rather 
than  with  affirmations,  and  see  blemishes  more  readily 
than  beauties.  They  are  largely  tolerant  in  theory, 
but  they  esteem  the  freedom  of  dissent  more  than 
the  freedom  of  conviction.  Such  persons  are  usually 
prone  to  speculation,  and  are  often  fruitful  in  in- 
genious suggestions ;  but  they  have  seldom  the  incli- 
nation or  the  patience  for  the  tedious  experimental 
work  required  to  verify  their  hypotheses.  They  are, 
as  a  rule,  highly  imaginative,  and  their  fancy  paints 
with  glowing  colors  every  subject  which  they  study ; 
but  their  deductions  are  not  always  trustworthy,  and 
their  generalizations  are  often  more  subtile  than  pro- 
found. They  are  sanguine  students,  and  their  enthu- 
siasm invests  their  teaching  with  a  peculiar  charm ; 
but  their  zeal  is  not  always  tempered  by  prudence, 
and  they  are  apt  to  be  better  expositors  of  what  is 


THE   POSITIVIST.  257 


known  than  investigators  of  what  is  unknown.  Men 
of  this  temperament  are  not  unfrequently  truly  liberal- 
minded,  capable  of  large  views,  and  fitted  to  be 
leaders ;  and  have  exerted  more  influence  on  the  ad- 
vancement of  knowledge  than  many  a  harder  student 
or  deeper  thinker. 

Then  there  is  another  class  of  scientific  students 
quite  different  from  either  of  the  two  types  we  have 
sketched,  and  one  which  the  specialism  of  our  day  is 
tending  very  greatly  to  multiply.  Among  this  class 
are  to  be  found  many  of  the  exact  anatomists  in 
natural  history,  the  accurate  analysts  in  chemistry, 
the  untiring  observers  in  astronomy,  men  who  do 
much  of  the  hard  work  of  science,  and  on  whose  un- 
swerving truthfulness  and  scrupulous  exactness  entire 
confidence  can  be  placed.  Minds  which  are  occupied 
with  minute  details,  which  delight  in  delicate  distinc- 
tions, and  find  pleasure  in  pushing  observations  to 
the  extreme  limit  of  accuracy,  are  apt  to  overlook 
the  broader  relations  of  truth,  and  value  only  definite 
results ;  and  it  is  among  such  students  that  the  posi- 
tive philosophy  finds  most  of  its  disciples.  The  class 
of  men  to  whom  we  refer  includes  not  only  those 
who  actually  avow  the  doctrines  of  positivism,  but 
also  those  who  cherish  a  similar  habit  of  mind,  — 
men  who  worship  facts  and  have  little  faith  in  ideals ; 
men  who  never  had  any  visions  themselves,  and  there- 
fore regard  all  visions  as  hallucinations  ;  men  to  whom 
the  material  is  the  only  reality,  and  the  spiritual  a 
dream.  Such  men  often  condemn  as  idle  specula- 
tions the  very  hypotheses  by  which  their  own  studies 
have   been   guided,   and   despise  the  theories  which 


258  THE   TRUE   SPIRIT. 

alone  give  significance  to  the  facts  that  have  cost 
them  so  dearly.  These  are  worthy  men  and  sincerely 
devoted  to  the  truth ;  but  their  range  is  narrow,  and 
their  prospect  restricted.  They  have  always  dwelt  in 
a  narrow  valley  amid  pleasant  pastures  and  beside 
still  waters.  They  have  never  ascended  unto  the  hills 
around  them ;  they  never  have  been  awed  by  the 
mountain  torrent;  they  never  have  been  oppressed 
by  the  mountain  gloom  ;  they  never  have  been  glad- 
dened by  the  mountain  vision. 

These  are  not  ideal  sketches  which  I  have  at- 
tempted to  draw.  They  are  lineaments  of  real  men, 
whose  biographies  you  may  read  in  the  history  of 
science ;  whom  you  may  meet  to-day  in  every  large 
society  of  scholars  ;  whom  you  all  must  have  known. 
Such  characters  are  not  the  products  of  scientific 
study  only.  They  are  equally  marked  in  every  de- 
partment of  learning.  In  politics  they  are  conserva- 
tists,  liberals,  or  bureaucratists.  In  philosophy  they 
become  realists,  nominalists,  or  positivists.  In  the- 
ology they  are  classed  as  low,  broad,  or  high  church ; 
and  they  are  recognized  as  conventionalists,  impres- 
sionists, or  preraphaelites  in  art.  We  must  seek  for 
the  origin  of  such  distinctions  far  down  in  the  varying 
dispositions  of  the  human  mind  and  in  the  influences 
of  education.  However  much  they  may  be  exagger- 
ated by  passion,  or  misguided  by  evil  counsel,  these 
traits  of  character  are  all  good  in  themselves ;  and 
when  blended  in  due  proportion,  they  make  the  Solons, 
the  Washingtons,  the  Shakspeares,  the  Miltons,  the 
Newtons,  the  Faradays,  of  history.  But  so  rarely  are 
such  qualities  of  mind  combined  that  we  often  regard 


THE  TRUE   SPIRIT.  259 

them  as  incompatible.  You  do  not  expect  to  find  in 
a  poet  that  attention  to  minute  details  which  marks 
the  man  of  affairs ;  nor  in  a  wise  counsellor  the  im- 
agination of  an  artist;  yet  in  the  great  pioneers  of 
science  such  opposite  faculties  have  been  united  in  a 
most  remarkable  degree.  They  have  been  men  of 
ideals,  but  men  whose  vivid  imaginations  were  regu- 
lated by  education,  and  chastened  by  wisdom.  They 
have  been  men  of  courage  and  perseverance,  who  fol- 
lowed out  their  convictions  through  every  discour- 
agement. They  have  been  men  of  entire  truthfulness 
who  have  never  hesitated  to  submit  their  doctrines  to 
the  test  of  crucial  experiments  and  to  abide  by  the 
issue.  They  have  been  men  of  the  most  scrupulous 
conscientiousness  in  attention  to  minute  details,  re- 
garding themselves  as  responsible  to  the  Giver  of  all 
truth  for  accuracy  in  every  observation,  and  for  ex- 
actness in  every  statement.  Finally,  they  have  been 
men  of  modesty  and  of  reserve  in  judgment,  realizing, 
as  no  other  men  ever  have,  how  boundless  is  truth ; 
how  limited  knowledge ;  how  intricate  the  problem 
of  nature ;  how  weak  in  comparison  the  intellect  of 
man. 


260  DICTATES   OF  EXPERIENCE. 


LECTURE    IX. 

PREDOMINANT   PRINCIPLES    OF   SCIENTIFIC 
THOUGHT. 

WE  have  already  in  the  preceding  lectures  dis- 
cussed at  some  length  the  validity  and  char- 
acter both  of  the  inductive  and  of  the  deductive  forms 
of  scientific  reasoning  ;  we  have  also  studied  the  au- 
thority and  relations  of  the  laws  of  nature,  as  well 
as  the  warrant  and  use  of  scientific  systems  ;  and  in 
order  to  complete  my  survey  of  the  general  methods 
of  science,  I  propose  lastly  to  consider  very  briefly 
certain  general  principles  by  which  students  of  nature 
have  been  greatly  guided,  and  which,  therefore,  have 
exerted  a  marked  influence  on  the  progress  of  knowl- 
edge. As  I  have  already  said,  the  mental  process  of 
induction  is  subject  to  no  known  laws  that  can  be 
accurately  defined.  It  is  a  product  of  genius  whose 
antecedents  we  can  rarely  trace,  and  whose  conditions 
we  can  seldom  analyze.  Nevertheless,  even  genius  is 
guided  by  experience ;  and  there  are  two  dictates  of 
experience  so  wide  in  their  application,  and  so  gen- 
erally trustworthy,  that  they  claim  our  notice  in  this 
connection.  I  refer  to  the  principles  of  analogy 
and  of  continuity,  which  although  often  found  deceit- 
ful guides,  yet  when  followed  with  caution  and  judg- 


ANALOGY.  26l 

ment  very  seldom  lead  astray.  Other  suggestions 
of  experience,  like  the  principles  of  least  waste,  of 
the  sufficient  reason,  of  successive  approach,  of  adap- 
tation, and  of  intelligent  plan,  have  been  found  at 
times  of  great  value  in  the  study  of  science;  but 
they  are  not  principles  so  generally  accepted  as 
those  first  named,  and  are  more  restricted  in  their 
application. 

There  can  be  no  question  that  the  suggestions  of 
analogy  have  led  to  more  discoveries  in  science  than 
all  other  influences  combined. 

If  the  force  of  the  earth's  gravitation  is  not  sensibly 
diminished  at  the  summits  of  the  highest  mountains, 
why  may  it  not  reach  to  the  moon?  Since  the  phe- 
nomena of  light  resemble  in  so  many  respects  those 
of  sound,  why  may  they  not  be,  like  these,  the  effects 
of  wave-motion?  If  there  be  in  masses  of  matter  an 
internal  molecular  motion  which  produces  thermal 
changes,  why  should  not  these  motions  obey  the  well- 
known  laws  which  govern  the  motions  of  the  masses 
themselves?  If,  as  Malthus  has  shown,  the  struggle 
for  existence  has  exerted  such  a  marked  influence  on 
the  history  of  the  human  race,  why  should  it  not 
produce  far  deeper  and  more  lasting  effects  among 
the  lower  animals,  where  the  struggle  is  vastly  more 
intense?  Thus  it  is  through  analogy  that  men  have 
been  led  to  each  of  the  great  systems  of  science 
now  dominant  in  the  intellectual  world.  So  also 
in  unnumbered  other  instances  analogy  has  given 
the  suggestion  which  observation  or  experiment  has 
verified. 

The   astronomer    noticed    through   the   telescope 


262  DECOMPOSITION   OF   THE   ALKALIES. 

patches  of  dazzling  whiteness  around  the  poles  of 
Mars;  and  since  this  planet  moves  around  the  sun 
under  relations  similar  to  those  of  the  earth,  he  in- 
ferred that  the  greater  brilliancy  was  caused  by  the 
reflection  of  light  from  snow-caps  like  those  which 
render  the  earth's  poles  so  inaccessible;  and  when  on 
watching  the  planet's  disk  from  year  to  year,  he  ob- 
served that  these  patches  alternately  increased  and 
diminished  with  the  changing  Martial  seasons,  he  felt 
assumed  that  this  suggestion  of  analogy  was  correct. 

Down  to  the  beginning  of  this  century  the  so-called 
earths  and  alkalies,  such  as  alumina,  magnesia,  lime, 
soda,  and  potash,  had  been  regarded  as  elementary 
substances ;  but  towards  the  close  of  the  last  century 
Lavoisier  had  shown  that  several  materials  closely 
resembling  the  earths,  such  as  iron-rust,  litharge, 
and  tinstone,  were  compounds  of  metals  with  the 
then  newly  discovered  oxygen  gas.  Analogy  at 
once  suggested  that  the  earths  and  alkalies  must  also 
contain  metals  united  to  oxygen ;  but  although  the 
analogy  inspired  a  confident  belief  in  this  inference, 
the  chemists  at  the  time  did  not  succeed  in  decom- 
posing the  compounds,  because  the  means  at  their 
command  were  inadequate.  But  the  discoveries  of 
Galvani  and  Volta  gave  the  world  a  new  agent  in 
voltaic  electricity,  which  by  the  decomposition  of 
water  proved  to  be  a  reducing  force  of  wonderful 
power;  and  the  first  moment  he  could  command  a 
voltaic  battery  of  sufficient  strength  Sir  Humphry 
Davy  applied  the  new  force  to  the  alkalies,  when  out 
at  once  the  metals  flowed. 

In  1812  iodine  was  discovered  by  Courtois  in  the 


SPECIFIC   FOR  GOITRE.  263 

crude  soda-salt  called  kelp,  which  is  prepared  by- 
burning  wrack,  and  is  simply  the  ashes  of  this  sea- 
weed. For  a  long  time  previously  burnt  sponge  had 
been  used  as  a  remedy  in  cases  of  goitre,  which  in 
the  mountainous  regions  of  Switzerland  produces 
such  wide-spread  and  distressing  results.  As  sponge 
in  its  habitat  and  relations  resembles  sea-weed,  anal- 
ogy suggested  that  the  burnt  sponge  might  contain 
a  minute  amount  of  iodine,  and  that  its  efficacy 
might  be  due  to  this  new  elementary  substance ;  and 
in  1820  Dr.  Coindet,  a  physician  of  Geneva,  aided  by 
the  young  chemist  Dumas,  succeeded  not  only  in 
proving  the  presence  of  iodine  in  the  sponge,  but  in 
replacing  a  nauseous  dose  by  preparations  of  iodine 
which  have  proved  almost  a  specific  for  the  terrible 
disease. 

Such  examples  might  be  multiplied  indefinitely; 
but  we  have  only  time  for  one  other,  which  is,  how- 
ever, very  striking.  As  we  have  before  said,  the  ele- 
mentary rays  of  a  beam  of  light  must  be  regarded  as 
moving  in  a  definite  plane;  and  a  beam  all  whose 
rays  are  moving  in  the  same  plane  is  said  to  be  po- 
larized. By  optical  means  we  can  readily  determine 
the  position  of  this  plane,  which  we  call  "the  plane 
of  vibration,"  sometimes  also  "  the  plane  of  polariza- 
tion." When  a  polarized  beam  of  light  passes  through 
a  plate  of  quartz  in  the  direction  of  the  axis  of  the 
well-known  hexagonal  crystals  of  this  mineral  the 
plane  of  polarization  suffers  a  rotation,  to  an  extent 
depending  on  the  thickness  of  the  plate.  Now  on 
some  of  the  hexagonal  crystals  .in  which  quartz  crys- 
tallizes there  are  to  be  found  certain  small  planes, 
is 


264  MAGNETIC   STRAIN. 

called  "  plagihedral,"  which  are  distributed  after  a 
helioidal,  or  spiral-like,  type  of  symmetry;  and  ac- 
cording as  the  spiral  ascends  to  the  right  or  to  the 
left,  the  plane  of  polarization  is  rotated  to  one  side  or 
to  the  other.  Remember  also  that  the  effects  of 
crystals  on  light  are  referred  by  the  undulatory 
theory  to  their  unequal  elasticity  in  different  direc- 
tions, and  that  similar  effects  can  be  obtained  with 
homogeneous  glass  by  subjecting  this  transparent 
material  to  unequal  strains,  and  thus  developing  un- 
equal elasticity  in  different  directions;  add  to  all  this 
the  further  fact  that  when  a  current  of  electricity  flows 
through  a  spiral  of  copper  wire  wound  round  a  bar 
of  iron,  and  renders  it  magnetic,  a  screw-like  strain  is 
developed  in  the  bar,  —  and  you  will  then  have  the 
basis  from  which  Sir  John  Herschel,  to  whom  these 
facts  and  theories  were  very  familiar,  inferred  by 
analogy  that  if  glass  or  other  transparent  material 
could  be  subjected  to  a  similar  magnetic  strain,  we 
might  obtain  under  such  conditions  the  same  effect 
of  rotating  the  plane  of  polarization  which  is  so 
markedly  exhibited  by  quartz;  and  further,  that 
possibly  such  a  strain  might  be  developed  by  a 
powerful  electro-magnet  Herschel  himself  never 
verified  this  suggestion  of  analogy;  but  the  effect 
was  subsequently  realized  in  a  most  striking  manner 
by  Faraday. 

The  validity  of  analogical  reasoning  unquestionably 
depends  on  the  harmonies  of  nature.  Since  the  uni- 
verse has  been  made  throughout  on  one.  plan,  and, 
however  varied  the  details,  the  same  general  patterns 
reappear  in  all  its  parts,  both  great  and  small,  we  can 


VALIDITY   OF  ANALOGICAL   REASONING.        265 


safely  infer  from  our  very  limited  experience  in  a 
narrow  field  what  are  the  conditions  and  relations  in 
remote  and  inaccessible  provinces  which  we  can 
never  directly  explore  with  our  senses.  Hence  it  is 
that  we  can  infer  that  molecules  and  atoms  obey  the 
same  laws  of  motion  as  suns  and  planets.  It  is 
wholly  conceivable  that  the  microcosmos  should 
have  been  planned  on  a  system  entirely  different 
from  that  of  the  macrocosmos;  but  apparently  the 
very  reverse  is  the  truth;  and  a  theory,  which  as- 
sumes that  within  the  masses  of  material  bodies  the 
motions  of  suns  and  systems  are  reproduced  on  a 
scale  so  minute  as  to  task  our  power  of  imagination 
to  grasp  the  conception,  is  found  to  be  in  complete 
accordance  with  all  the  facts  which  can  be  observed. 
Moreover,  whenever  we  have  been  able  to  obtain  evi- 
dence we  have  found  our  reliance  on  the  unity  of 
nature  fully  justified. 

Within  a  comparatively  {ew  years  our  confidence 
in  this  regard  has  been  very  greatly  strengthened  by 
the  revelations  of  the  spectroscope.  If  our  globe 
was  once  thrown  off  from  the  sun  we  might  expect 
that  it  would  be  a  chip  of  the  old  block ;  but  we  can 
conceive  of  no  necessity  which  requires  that  the  ma- 
terials of  the  fixed  stars  should  be  like  that  of  our 
earth.  Still,  the  spectroscope  tells  us  that  in  those 
immensely  distant  bodies  the  same  elementary  sub- 
stances are  glowing  with  which  we  are  so  familiar  in 
our  laboratories.  And  if  anywhere  in  the  depths  of 
space  there  revolves  around  one  of  those  centres  of 
energy  a  globe  which  has  been  reduced  to  the  cli- 
matic conditions  of  our  earth,  we  can  infer   with  a 


266        VALIDITY   OF  ANALOGICAL   REASONING. 

confidence  which  approaches  certainty  that  its  rocks 
contain  the  same  minerals,  and  that  its  plants  and 
animals  are  fashioned  after  the  same  patterns  with 
which  we  are  so  familiar;  and,  if  it  has  also  become 
the  abode  of  intelligent  beings,  that  they  have  been 
discussing  the  same  great  problems  which  have  per- 
plexed man. 

It  is  solely  the  unity  and  harmony  of  nature  which 
renders  analogical  reasoning  valid.  To  this  harmony 
our  own  being  answers,  and  it  is  only  because  we  are 
in  unison  with  nature  that  we  are  able  to  interpret  her 
methods.  Were  our  minds  not  in  harmony  with  our 
surroundings,  or  those  surroundings  not  in  harmony 
with  the  rest  of  creation,  our  intelligences  would  have 
been  confounded,  and  all  nature  would  have  been  to 
us  a  sealed  book. 

Man  cannot  conceive  in  a  concrete  form  of  any- 
thing he  has  not  previously  received  through  the 
senses.  No  hypothesis  can  be  so  much  as  framed 
in  the  mind  which  has  not  some  semblance  in  pre- 
vious experience ;  and  as  through  our  senses  we  have 
direct  cognizance  only  of  material  things,  we  cannot 
picture  to  ourselves  any  existences  without  associ- 
ating with  them  some  of  the  qualities  of  matter.  The 
most  we  can  do  is  to  alter  the  combinations  of  our 
experience,  or  to  change  in  degree  the  qualities  we 
have  actually  observed.  This  is  all  we  have  done  in 
forming  the  most  subtile  conception  man  has  ever 
grasped,  —  that  of  the  luminiferous  ether.  We  are 
familiar  with  elasticity,  and  we  can  predicate  an 
elasticity  a  million  or  a  billion  times  greater  than 
any  that  is  known  to  us.     We  know  what  density 


FAILURES   OF  ANALOGY.  267 

is,  and  we  can  at  least  in  words  describe  a  material 
less  dense  than  any  known  substance  in  a  similar 
extreme  degree,  and  then  in  imagination  combine 
these  extravagances.  But  what  we  reach  is  a  con- 
dition of  matter,  and  all  our  calculations  in  regard 
to  it  are  based  on  its  likeness  to  matter.  We  can,  in 
imagination,  vary  the  known  qualities  of  matter  to 
an  unlimited  degree.  We  can  combine  these  quali- 
ties in  other  than  the  accustomed  relations.  But, 
however  much  we  may  think  or  talk  about  other 
states  of  existence,  we  cannot  actually  picture  to 
ourselves  any  existence  or  mode  of  action  of  which 
experience  has  not  given  us  some  semblance.  Thus 
all  our  science  —  that  is,  our  knowledge  of  things  — 
rests  on  experience,  and  never  could  have  been  built 
up  had  not  the  unknown  been  of  a  piece  with  the 
known. 

But  while  analogy  is  thus  the  guiding  rule  of  sci- 
entific thought,  it  is  a  rule  which  cannot  be  blindly 
followed.  The  suggestions  of  analogy  have  often 
proved  delusive,  —  either  because  the  resemblances 
on  which  we  counted  were  superficial  and  not  real, 
or  because  our  scientific  methods  and  appliances 
were  inadequate  to  establish  the  relations  we  sus- 
pected. The  history  of  science  is  full  of  examples 
of  misdirected  efforts  whose  failure  is  to  be  attri- 
buted to  one  or  the  other  of  these  causes.  Two 
marked  instances  will  serve  as  illustrations. 

After  the  elder  Herschel  with  his  large  telescope 
had  distinguished  in  several  of  the  nebulas  points  of 
light,  and  later  Lord  Rosse  with  a  much  larger  re- 
flector had  resolved  still  more  of  these  distant  star- 


268  FAILURES   OF   ANALOGY. 

clusters,  it  was  inferred  by  astronomers  that  all  the 
nebulae  were  groups  of  stars,  whose  resolution  was 
only  a  question  of  telescopic  power.  But  since  the 
application  of  the  spectroscope  to  the  problem  it 
has  been  found  that  there  is  a  very  large  class  of 
these  objects  which  are  masses  of  luminous  vapors ; 
and  it  is  evident  that  the  astronomers  were  at  first 
deceived  by  a  superficial  resemblance. 

Faraday,  after  he  had  investigated  with  such  con- 
summate skill  the  relations  of  electricity  to  mag- 
netism, conceived  that  similar  relations  must  exist 
between  these  modes  of  energy  and  gravitation ;  and 
devoted  a  great  deal  of  labor  and  thought  to  the  in- 
vestigation of  the  subject.  He  made  several  series 
of  laborious  experiments  in  the  clock-tower  of  the 
Houses  of  Parliament  and  elsewhere,  but  with  abso- 
lutely no  results.  To  use  his  own  words,  "The 
experiments  were  well  made,  but  the  results  are 
negative;  "  but  he  adds,  "  I  cannot  accept  them  as 
conclusive."  So  the  question  remains  to  the  present 
day ;  and  it  is  possible,  as  Faraday  evidently  believed, 
that  the  failure  arose  from  the  want  of  appliances 
sufficiently  delicate  to  show  the  expected  effects; 
although,  if  the  opinion  previously  expressed  in 
these  lectures  in  regard  to  the  nature  of  gravity  be 
correct,  it  was  the  seeming  analogy  which  was  at 
fault,  as  Faraday  himself  at  times  suspected. 

In  his  failures  not  less  than  in  his  successes,  the 
example  of  Faraday  may  teach  us  most  important 
lessons.  A  mind  so  subtile  as  his  is  apt  to  be  capti- 
vated by  fanciful  resemblances;  but  he  never  fol- 
lowed vaguely  the  suggestions  of  analogy,  inquiring 


GENERALIZATION.  269 

diligently  at  every  step  whither  they  were  leading, 
and  always  submitting  desire  to  the  control  of"  ex- 
perience. As  thus  curbed,  analogy  may  be  always 
safely  followed;  and  as  Bishop  Butler  so  tersely 
wrote,  "  Analogy  is  the  very  guide  of  life."  She 
leads  us  when  we  are  least  aware  of  her  guidance. 
She  colors  all  our  language.  She  determines  half 
our  thoughts.  In  submitting  ourselves,  as  we  must, 
to  her  control,  let  us  consider  well  the  situation ;  and 
while  we  acknowledge  our  dependence,  never  part 
with  our  more  precious  birthright.  Our  guide  is 
moulded  of  the  same  clay  as  ourselves;  and  there 
may  be  things  in  earth,  as  well  as  in  heaven,  not 
dreamt  of  in  her  philosophy.  And,  moreover,  if 
harmony  with  nature  be  a  test  of  reality,  then  har- 
mony with  the  spiritual  life,  then  adaptation  to  the 
needs  of  the  soul,  is  also  a  mark  of  certitude,  an 
equally  overpowering  evidence  of  truth. 

Generalization  in  science  is  only  a  form  of  ana- 
logical reasoning.  We  are  said  to  generalize  when 
we  ascribe  to  a  class  of  objects  qualities  or  relations 
which  have  been  shown  to  be  true  of  certain  charac- 
teristic members  of  the  class.  Thus  a  certain  num- 
ber of  substances  having  a  brilliant  lustre,  and  to  a 
greater  or  less  degree  ductile  or  malleable,  and  at 
the  same  time  good  conductors  of  heat  and  elec- 
tricity, which  we  class  under  the  general  name  of 
metals,  have  been  found  after  repeated  trials  to  resist 
every  attempt  to  decompose  them,  and  are  therefore 
regarded  as  elementary  substances.  Hence  we  con- 
clude that  all  metals  are  elementary  substances ;  and 
when  a  new  one  is  discovered,  as  is  not  unfrequently 


2/0 


GENERALIZATION. 


the  case,  we  never  think  of  attempting  to  analyze  it, 
because  experience  with  similar  bodies  assures  us 
that  all  such  attempts  would  be  fruitless. 

Again,  it  has  been  shown  by  Davy,  Wohler,  and 
others,  that  alumina,  magnesia,  and  several  of  the  simi- 
lar earths  are  metallic  oxides,  and  the  metals  of  which 
they  consist  have  been  extracted  and  studied;  indeed 
aluminum  and  magnesium  are  now  articles  of  com- 
merce and  familiar  to  every  one.  Hence  we  con- 
clude that  all  amorphous  powders  resembling  alumina 
and  magnesia,  and  having  like  chemical  properties 
are  also  metalliferous;  so  that  when,  within  a  few 
years,  a  large  number  of  new  earths  were  distinguished 
the  chemist  accepted  them  at  once  as  metallic  oxides, 
although  in  most  cases  the  metal  has  not  actually 
been  isolated. 

Obviously,  our  assurance  in  all  these  cases  rests  on 
our  confidence  in  the  unity  of  nature's  plan  and 
method ;  and  the  argument  which  convinces  us  dif- 
fers from  the  ordinary  argument  from  analogy  only 
in  the  extent  of  the  ground  covered.  When  Davy 
inferred  from  analogy  that  potash  must  contain  a 
metal,  and  successfully  followed  out  the  suggestion, 
he  reasoned  from  a  comparatively  superficial  resem- 
blance between  a  few  things  to  a  deeper  relationship. 
When  we  conclude  that  the  new  earths  are  metallic 
oxides,  we  reason  from  a  wide  knowledge  of  a  class  of 
bodies  that  a  new  substance,  which  has  been  shown  to 
have  the  other  qualities  and  relations  of  this  class, 
also  has  an  additional  character,  —  though  as  yet  un- 
observed,—  which  is  common  to  all  the  other  mem- 
bers therein  grouped.    The  reasoning  in  the  last  case 


ALL   KNOWLEDGE   RELATIVE.  2"Jl 

is  far  more  conclusive  than  in  the  first ;  but  evidently 
it  rests  on  the  same  assurance,  the  uniformity  of  nature. 
Prior  to  experiment  Davy's  inference  was  only  proba- 
ble ;  our  conclusion  is  as  certain  as  that  the  sun  will 
rise  to-morrow.  In  either  case,  however,  the  argu- 
ment is  based  on  resemblances  more  or  less  remote, 
and  the  difference  is  one  of  degree  and  not  of  kind ; 
and  so  we  may  have  every  degree  between  the  certi- 
tude of  a  far-reaching  generalization  and  the  mere 
suggestion  of  a  feeble  analogy.  In  science  the  merest 
hint  maybe  of  value;  for  when  in  an  investigation 
bewildered  by  complex  conditions  we  are  hesitating 
which  way  to  turn,  or  what  to  try  first,  the  faintest 
suggestion  of  analogy  may  decide  us.  On  the  other 
hand,  in  the  relations  of  the  spiritual  life  we  must 
remember  that  even  in  our  grandest  generalizations 
we  cannot  escape  from  the  material  clogs  of  our  mor- 
tal experience;  that  all  our  knowledge  is  necessarily 
relative  to  our  environment;  and  that  though  its 
material  forms  are  doubtless  symbols  of  higher  reali- 
ties, yet  these  earth-born  fancies  can  never  be  an 
exact  picture  of  things  spiritual,  or  a  precise  measure 
of  things  divine. 

Man  lives  in  time,  and  he  cannot  release  his 
thoughts  from  the  fetters  which  this  condition  im- 
poses. Continuous  time  and  a  corresponding  con- 
tinuous change  or  growth  are  so  inseparable  from 
human  experience  that  existence  in  time,  with  pro- 
gressive change,  is  the  only  mode  of  being  of  which 
the  mind  can  form  a  concrete  idea.  We  can  reason 
and  talk  about  a  Being  who  is  the  same  yesterday, 
to-day,  and  forever,  and  to  whom  a  thousand  years 


272  PRINCIPLE   OF   CONTINUITY. 

are  as  one  day  and  one  day  as  a  thousand  years, — 
we  firmly  believe  in  the  reality  of  such  a  Being;  but 
we  cannot  picture  the  existence  to  our  minds,  as  the 
very  imagery  plainly  shows.  As  we  cannot  escape 
from  the  limitations  of  matter,  so  we  cannot  escape 
from  the  limitations  of  time.  As  regards  every  event, 
the  mind  demands  an  antecedent  and  a  consequent. 
The  common  axiom  that  "  every  event  must  have  a 
cause  "  is  another  phase  of  the  necessity  which  the 
conditions  of  our  environment  impose  on  our  being. 
The  necessity  is  so  interwoven  in  the  complex  web  of 
material  existence  that  we  cannot  dissociate  it  if  we 
would.  It  is  not  a  necessity  of  thought;  for  that 
Being  who  is  from  eternity  to  eternity  the  same  had 
no  antecedent  and  no  cause.  But  it  is  a  necessity  of 
the  imagination,  and  therefore  a  necessity  of  scientific 
knowledge. 

In  science  we  call  this  lesson  of  experience  "  the 
principle  of  continuity,"  and  it  is  a  belief  which 
exerts  a  profound  influence  on  all  our  reasoning  about 
material  relations.  It  is  this  principle  which  alone 
gives  strength  to  the  doctrine  of  evolution ;  but  it  is 
equally  a  controlling  power  in  almost  every  depart- 
ment of  scientific  inquiry  ;  indeed  it  controls  the 
very  process  of  thought  itself. 

Examples  of  continuity  of  action  are  all  around  us, 
and  illustrations  of  the  successful  application  of  the 
principle  in  scientific  reasoning  might  readily  be 
cited.  The  science  of  geology  is  especially  rich  in 
examples  of  this  class  ;  and  our  knowledge  of  the 
relative  ages  of  strata,  and  of  the  succession  of  life  on 
the  earth,  is  in  very  large  measure  the  result  of  tracing 


BREAKS   OF   CONTINUITY.  273 

out  the  evidences  of  continuous  changes  ;  and  in 
physics  we  often  reason  from  what  we  can  see  to 
what  we  cannot  see,  through  a  chain  of  sequences 
which  connects  the  parts  of  a  continuous  series,  and 
thus  exhibits  relations  which  would  be  otherwise 
obscure.  The  same  principle  underlies  all  classifica- 
tion in  natural  history,  and,  as  has  been  already 
said,  is  the  warrant  of  the  theory  of  evolution. 
Evolution  is  simply  a  wider  growth,  and  is  implied 
in  the  only  conception  of  being  of  which  the  mind 
can  frame  a  definite  image.  For  our  purpose,  how- 
ever, it  is  not  necessary  to  multiply  illustrations ;  and 
we  turn  next  to  some  examples  of  the  break  of  con- 
tinuity which  have  a  much  more  important  bearing 
on  our  subject ;  for  they  indicate  that  beneath  the 
obvious  material  relations  there  may  be  other  influ- 
ences at  work  in  determining  the  course  of  events. 

While  we  can  usually  safely  follow  the  indications 
of  continuity,  yet,  as  in  the  case  of  analogy,  we  are 
frequently  deceived,  and  even  more  frequently  than 
in  the  application  of  the  cognate  principle  ;  and  ex- 
amples of  break  of  continuity  present  a  striking  feat- 
ure of  nature  which  cannot  be  overlooked.  Often 
the  break  is  only  apparent,  resulting  from  the  inabil- 
ity of  our  senses  to  follow  changes  succeeding  each 
other  with  more  than  a  certain  limited  rapidity. 
When  a  ball  is  fired  from  a  rifled  cannon  it  gains  in 
the  two  hundredth  part  of  a  second  its  full  and  fearful 
velocity,  and  yet  we  know  that  while  in  the  gun  it 
passed  through  every  stage  of  motion  from  indefinite 
slowness  onwards.  So  also  with  molecular  motions, 
which  may  last  only  some  thousand  millionths  of  a 


274  CRYSTALLIZATION. 

second ;  between  successive  collisions  all  the  phases 
of  the  recoil,  the  free  path,  and  the  rebound,  must 
follow  each  other  in  due  order. 

We  do  however  find  in  nature  phenomena  which, 
after  making  every  allowance  for  the  imperfection  of 
our  senses,  appear  to  be  absolute  breaks  of  continuity. 
One  of  the  most  striking  of  these  is  to  be  seen  in 
the  process  of  crystallization.  I  confess  that  I  never 
witness  the  process  without  amazement.  That  out  of  a 
perfectly  homogeneous  and  structureless  liquid  there 
should  suddenly  separate  a  perfect  geometrical  solid, 
with  all  its  sparkling  facets  grouped  with  mathemati- 
cal exactness,  is  to  me  one  of  the  greatest  wonders  in 
this  world  of  beauty.  The  structure  of  a  crystal  is  of 
course  not  so  complex  as  that  of  a  plant  or  an  ani- 
mal; but  then  it  has  no  gradual  genesis;  it  has  no 
antecedents ;  it  appears  as  a  sudden  break  of  con- 
tinuity; its  formation  approaches  as  near  to  a  sudden 
creation  as  anything  we  ever  behold.  This  may  seem 
to  you  inconsistent  with  what  you  have  heard  of  the 
slow  growth  of  crystals.  But  such  statements  apply 
only  to  the  large,  massive  crystals,  such  as  you  may 
see  in  our  museums,  —  some  of  which  have  doubtless 
been  centuries  in  forming.  I  refer,  on  the  contrary, 
to  the  sudden  production  of  the  minute  crystals  of 
which  the  larger  crystals  are  gradually  formed  aggre- 
gates. These  small  crystals,  when  examined  with  a 
microscope,  are  seen  to  be  as  perfect  as  the  larger 
specimens  ;  indeed,  they  are  often  far  more  per- 
fect; and  they  seem  to  drop  out  of  the  solution  in- 
stantaneously,—  the  creation  of  each  one,  if  I  may 
dare  to  use  the  term,  being  in  some  cases  attended 


DEFINITE   PROPORTIONS.  275 


with   a  flash  of  light  as  if  to    attest  its   mysterious 
origin. 

Another  circumstance  which  sometimes  attends  on 
crystallization  is  even  more  indicative  of  a  break  of 
continuity  than  the  facts  I  have  mentioned.     In  the 
liquid  menstruum,  as  it  is  called,  the  constituents  of 
the  future  crystal  are  often  mixed  in  variable  propor- 
tions ;  but  the  crystals  which  form  unite  these  ingre- 
dients in  absolutely  definite  proportions,  conforming 
to  the  great  law  of  combining  proportions  of  chem- 
istry.    This  law  in  itself  is  probably  the  most  general 
and  striking  break  of  continuity  in  nature.  You  may 
mix  two  substances,  by  solution  or  otherwise,  in  any 
proportions  whatever,  and  there  appears  to  be  a  per- 
fect interpenetration  of  the  masses.     Then  when  an 
electric  spark,  or  some  other  cause,  determines  chem- 
ical union,  these  substances  unite  in  certain  constant, 
definite,  and  calculable,  proportions,  excluding  the 
excess  of  one  or  the  other  ingredient;    and  this  is 
what  takes  place  tin  the  example  of  crystallization 
just  referred  to.     In  order  to  reconcile  this  striking 
phenomenon  with  the  principle  of  continuity,  several 
chemists  have  endeavored  to  show  that  these  definite 
proportions  were  merely  a  maximum  effect  of  such 
restricted  range  that  we  failed  to  recognize  the  grada- 
tions ;   and  I  have  myself  sought  to  test  this  sugges- 
tion by  experimenting,  —  thinking  that  the  range  must 
be  greater  in  proportion  as  the  combining  force  was 
feebler,  and  that  possibly  in  cases  of  weak  chemical 
affinity  it  might  be  detected.     But  although  at  first  I 
thought  I  discovered  an  indication  of  such  an  effect, 
my  later  experiments  have  proved  that  the  propor- 


276  NATURAL   AND    SUPERNATURAL. 

tions  are  just  as  definite  in  weak  compounds  as  in 
strong.  I  see  therefore  no  escape  from  the  conclu- 
sion that  this  apparent  break  of  continuity  is  a  real- 
ity; and  should  not  such  results  teach  us  that  the 
preconceptions  of  our  experience  are  not  infallible? 
Thus  may  even  the  study  of  science  prepare  us  to 
recognize  other  possibilities  of  being  than  those  of 
known  material  relations. 

That  mode  of  being  not  directly  cognizable  by  our 
senses  we  call  the  supernatural;  and  we  often  reason 
as  if  it  were  something  apart  from  and  above  nature. 
But  is  it  not  the  more  consistent  theory  that  the  su- 
pernatural and  the  natural  are  simply  different  phases 
of  one  system  ;  and  that  while  with  our  bodily  senses 
we  apprehend  only  the  material  relations  of  this  sys- 
tem, we  can  with  our  spiritual  sympathies  and  aspira- 
tions reach  out  towards  those  higher  associations 
for  which  this  life  is  a  preparation?  Or  may  we  not 
rather  say  that  the  supernatural  embraces  the  natural, 
modifying  in  numberless  ways  the  more  obvious  ma- 
terial relations,  and  thus  constantly  apprising  us  of 
its  omnipresence ;  and  do  not  such  indications  as  we 
have  been  studying  ever  remind  us  that  the  material 
is  not  all  of  knowledge  or  all  of  life,  and  give  us  a 
confident  expectation  of  more  life  and  ampler  knowl- 
edge behind  the  vail? 

When  we  fully  comprehend  that  the  fundamental 
conceptions  comprised  under  the  doctrine  of  con- 
tinuity are  simply  a  product  of  experience,  and 
dependent  on  material  relations,  we  shall  be  able  to 
think  and  reason  more  justly  about  spiritual  relations 
in  which  the  limitations  of  the  material  do  not  exist ; 


IDEA   OF  TIME.  277 


and  although  difficulties  of  conception  may  by  no 
means  be  removed,  yet  a  way  is  opened  by  which 
the  seeming  contradictions  of  theological  doctrines 
with  our  experience  may  possibly  be  reconciled. 

As  has  already  been  intimated,  we  have  no  expe- 
rience, and  therefore  no  actual  knowledge,  of  any 
state  of  existence,  except  of  that  in  which  continuous 
change  and  growth  constitute  the  invariable  order 
of  being.  Our  idea  of  time  is  simply  a  conception 
based  on  the  succession  of  events.  The  fundamental 
conception  of  duration  arises  unquestionably  from 
the  succession  of  thoughts  in  our  own  minds.  It  is 
thus  that  we  reach  an  idea  of  short  duration,  as  of 
the  swing  of  a  pendulum;  and  it  is  only  of  such 
durations  that  we  can  be  said  to  have  any  direct 
consciousness.  Longer  durations  are  to  us  simply 
the  multiples  of  such  short  intervals  as  we  can  di- 
rectly perceive  and  appreciate ;  or  else  have  known 
relations  to  the  periods  of  events  which  we  assume 
as  the  standards  of  measure.  The  day  is  the  period 
of  the  rotation  of  the  earth  on  its  axis ;  the  hour  is 
one  twenty-fourth  part  of  a  day,  the  minute  the  one 
sixtieth  part  of  an  hour;  the  second  the  one  sixtieth 
part  of  a  minute,  and  at  any  given  place  is  the  dura- 
tion of  the  swing  of  a  pendulum  (about  one  meter 
long),  whose  exact  length  is  easily  adjusted.  It  is 
only  this  smallest  unit  of  which  we  can  be  said  to 
have  any  direct  perception.  Our  knowledge  of  much 
larger  periods,  however  exact,  is  purely  formal. 
When  a  boy  learns  that  a  year  is  the  period  of  the 
revolution  of  the  earth  around  the  sun,  the  most  he 
gains  is  the  idea  that  this,  to  him  already  familiar 


278  TRUE   MEASURE   OF   LIFE. 

period  ia  human  relations,  during  which  the  succes- 
sion of  seasons  is  completed,  is  the  duration  of  a 
continually  recurring  astronomical  event.  Nor  does 
his  knowledge  become  any  more  real  when  he  is 
further  informed  that  the  year  comprehends  three 
hundred  and  sixty-five  days,  five  hours,  forty-eight 
minutes,  forty-seven  and  seven  tenths  seconds.  But 
he  can  be  thus  impressed  with  the  fact  that  the 
durations  of  the  events  by  which  time  is  measured 
bear  a  constant  relation  to  each  other,  and  hence,  be 
led  to  the  conclusion  that  the  quantity  measured  is 
a  real  attribute  of  material  relations,  and  hence,  also 
of  material  life. 

A  very  few  considerations,  however,  will  show  that 
time  is  solely  an  attribute  of  material  relations,  and 
no  adequate  measure,  even  of  that  phase  of  our 
spiritual  life  which  terminates  with  the  death  of  the 
mortal  body.  Conventionally,  we  measure  man's  life 
in  years ;  but  who  does  not  recognize  that  Raphael, 
dying  at  thirty-seven,  or  Pascal,  dying  at  thirty-nine, 
lived  not  only  a  richer,  but  a  really  longer  life  than 
most  of  the  Methuselahs  and  Nestors  of  history.  He 
lives  longest  who  is  able  most  fully  — 

"  To  crowd  the  narrow  span  of  life, 
With  wise  designs  and  glorious  deeds." 

Life  should  be  measured  not  by  years,  but  by 
thoughts,  events,  and  deeds.  The  succession  of 
thoughts  in  the  mind  is  a  far  more  accurate  measure 
of  conscious  duration  than  the  beats  of  a  pendulum; 
although  as  compared  with  the  standard  of  time,  the 
flow  of  thoughts  is  so  variable,  not  only  in  the  minds 


RAPIDITY   OF  THOUGHT. 


279 


of  different  men,  but  also  in  our  own  minds  under 
varying  conditions.  After  some  critical  experience, 
how  often  do  we  say  that  we  have  lived  longer  during 
the  past  day  or  week  than  during  months  or  years 
before;  and  these  words  are  no  mere  figure  of  speech, 
but  on  the  contrary  express  an  important  truth. 

During  our  mortal  lives,  the  rapidity  of  thought  is 
limited  by  our  physical  organization;    but  we  can 
easily   conceive   that    it    might    be    indefinitely   in- 
creased ;  and  such  conceptions  appear  in  part  to  be 
realized  both  in  the  phenomena  of  dreams,  and  in 
the  experience  of  drowning  men ;  who,  when  subse- 
quently resuscitated,  often  have  said  that,  during  the 
brief  interval  before  they  became  unconscious,  the 
whole  course  of  their  lives  flashed  through  the  mind. 
Could   we   increase   the    rapidity   of  thought,   we 
should  increase  the  conscious  duration  of  life  during 
a  given  time ;  and  it  is  a  perfectly  rational  concep- 
tion, that  with  a  finer  organization  the  life  of  a  cen- 
tury might  be  crowded  into  a  day.     Obviously,  we 
can  apply  magnifying  power  to  time  as  we  can  to 
extension.      As    under    our    microscopes,    an    area 
barely  perceptible  to  the  eye  becomes  spread   out 
into  a  broad  plane,  teeming,  it  may  be,  with  life,  so 
we  can  conceive  that  a  duration  barely  perceptible  to 
our  senses  may  be  to  a  more  delicate  organism  a 
period  of  vast  activities. 

"  Alike  in  God's  all-seeing  eye, 
The  infant's  day,  the  patriarch's  age." 

Magnify,  now,  duration  indefinitely,  not  by  extend- 
ing time,  but  by  crowding  activities  into  the  present, 
T9 


230  LIMITATIONS    OF   TIME  AND   SPACE. 

and  you  annihilate  time,  —  or  rather,  you  eliminate 
the  element  of  time  from  the  spiritual  life;  and  such 
considerations  will  lead  the  mind  to  recognize  the 
truth  that  eternity  consists  not  in  limitless  time, 
which  would  be  unendurable,  not  in  passionless  con- 
templation, which  would  be  weariness,  but  in  the 
removal  of  the  limitations  of  time  from  our  mental 
activities.  Time,  like  space,  is  an  attribute  of  material 
relations ;  and  although  in  this  life  even  our  mental 
processes  are  controlled  by  the  limitations  which 
these  relations  impose,  and  although  the  imagination 
can  form  no  distinct  image  of  a  state  of  being  freed 
from  the  limitations  of  time  and  space,  yet  we  are 
able  by  such  considerations  as  we  have  here  imper- 
fectly presented  so  far  to  dissociate  in  our  thoughts 
these  conditions  from  our  spiritual  life  as  to  recog- 
nize the  aptness  of  the  imagery  by  which  such  a 
state  is  prefigured  in  the  Scriptures,  and  also  to  ad- 
mit the  possibility  of  spiritual  relations  which  to  our 
material  vision  seem  to  be  contradictory.  We  can- 
not be  said  to  have  actual  knowledge  of  any  state  of 
being  unconditioned  by  time  and  space ;  but  the 
circumstance  that  we  are  able  to  recognize  some  of 
the  attributes  of  such  a  state  is  in  itself  weighty 
evidence  of  its  reality. 

To  a  being  freed  from  the  limitations  of  time  there 
are  no  beginnings  and  no  ends ;  or  rather,  those  tran- 
sitions which  to  us  appear  as  the  beginnings  or  the 
ends  of  events,  are  simply  phases  of  the  ever  present 
and  the  ever  actual.  God's  prescience  is  not  fore- 
knowledge, but  actual  knowledge.  He  seeth  the  end 
from  the  beginning,  because  both  are  ever  present; 


FREE  WILL.  28l 


and  His  knowledge  is  not  inconsistent  with  man's 
free  will,  because  that  will  is  limited  in  its  exercise 
by  the  very  conditions  of  time  and  space  which  the 
Creator  has  imposed  on  the  material  universe. 

In  all  material  relations  man's  free  will  is  a  definite 
factor,  as  much  so  as  any  other  form  of  energy;  and 
the  final  attitude  of  man's  mind  towards  his  Maker  is 
equally  within  his  own  power  of  determination ;  but 
here  man's  prerogative  stops.  Man  as  a  living  creat- 
ure has  a  subordinate  power  in  the  material  creation. 
Man  as  a  living  soul  may  regulate  the  attitude  of  his 
mind  to  other  living  souls ;  but  however  completely 
he  may  control  actions,  he  cannot  force  the  wills  even 
of  those  nearest  and  dearest  to  himself.  In  a  word, 
his  will  has  control  only  over  material  relations  and 
over  himself;  and  to  one  who  does  not  wait  on  re- 
sults, but  who  sees  at  once  every  stage  of  our  material 
processes  and  of  our  mental  conflicts,  the  foreknowl- 
edge of  events  may  be  perfectly  consistent  with  the 
freedom  of  His  subordinate  actors  in  the  drama  of 
human  life.  The  architect,  who  in  his  imagination 
sees  his  building  completed  in  all  its  details,  may  be 
said  to  have  a  foreknowledge  which  is  compatible 
with  a  large  degree  of  freedom  among  the  workmen 
in  their  respective  spheres ;  and  although  this  illus- 
tration fails  in  essential  details,  it  may  serve  to  pre- 
figure that  fuller  prescience  when  the  limitations  which 
here  exist  are  removed. 

Such  illustrations  do  not  of  course  remove  the  diffi- 
culty we  have  in  conceiving  of  a  being  freed  from  the 
limitations  of  time ;  and,  by  dwelling  on  the  thought 
that  it  is  impossible  that  we  should  be  free  if  God 


UNREALIZED   INFERENCES. 


foresees  all  our  actions,  we  can  easily  make  the  in- 
compatibility appear  as  marked  as  ever.  All  that  we 
can  hope  is  to  recognize  the  possibility  of  conditions 
which  may  make  such  relations  intelligible,  without 
expecting  to  comprehend  them.  Free  will  is  a  fact 
of  consciousness,  and  such  considerations  as  we  have 
advanced  make  God's  foreknowledge  a  clear  inference 
of  our  intelligence  from  facts  of  consciousness;  and 
here  as  elsewhere  we  must  be  content  to  accept  our 
limitations,  and  wait  for  the  clearer  day  when  we  shall 
know  even  as  we  are  known. 

It  is  not  solely  in  spiritual  relations  that  our  reason 
leads  us  to  inferences  which  lie  beyond  the  powers  of 
conception.  This  is  equally  the  case  in  the  higher 
forms  of  mathematics,  where,  as  we  have  before  said, 
we  often  deal  with  relations,  like  the  higher  dimen- 
sions of  multiple  algebra,  of  which  it  is  impossi- 
ble for  the  mind  to  form  any  distinct  idea;  and  no 
mathematician  questions  that  these  relations  are  re- 
alities, yet  he  can  only  describe  them  by  inadequate 
and  figurative  language  which  deals  with  types  and 
symbols. 

This  power  of  the  human  mind  of  reaching  out  in 
various  directions  beyond  its  own  experience,  to  rela- 
tions of  which  it  can  form  no  concrete  and  material 
images,  is  to  my  own  mind  one  of  the  strongest  evi- 
dences of  the  reality  of  a  higher  life  in  which  these 
dim  visions  shall  be  realized. 

We  do  not,  however,  care  to  deal  with  theological 
subtleties;  but  the  overlooking  of  the  distinction  be- 
tween the  material  and  the  immaterial,  which  we  have 
attempted  to  emphasize,  has  led  to  a  fallacy  in  much 


MISTAKEN   PRECONCEPTION.  283 

of  the  reasoning  about  the  genesis  of  nature  which  it 
is  important  to  expose. 

We  can  form  no  clear  conception  of  any  act  except 
as  taking  place  at  a  given  time.  The  battle  of  Water- 
loo was  fought  June  18,  181 5.  America  was  discov- 
ered on  the  12th  of  October,  1492.  Julius  Caesar 
was  assassinated  in  the  ides  of  March,  44  B.  c.  The 
battle  of  Marathon  was  fought  September  28  or  29 
(according  to  somewhat  uncertain  computations), 
490  B.C.;  and  the  popular  belief  is  that  the  world 
was  created  at  an  equally  definite  date  in  the  remote 
past,  which  could  be  stated  in  equally  precise  chro- 
nology if  we  only  had  the  knowledge.  At  the  basis 
of  this  belief  is  a  tacit  assumption  that  all  intelligence, 
the  Creator  as  well  as  the  creature,  must  act  under 
the  limitations  of  time.  "  God  spake  and  it  was 
done;  "  and  we  assume  that  the  word  of  the  Creator, 
like  the  word  of  man,  was  spoken  at  a  definite  mo- 
ment in  the  succession  of  events  which  measure 
time.  But  science  shows  that  the  genesis  of  the 
world  was  a  process  of  gradual  growth ;  and  the  in- 
consistency of  this  conclusion  in  a  great  variety  of 
phases  with  man's  preconception  of  the  mode  of 
creation,  has  always  been  a  hindrance  to  faith. 

It  is  by  no  means  perfectly  clear  how  such  a  gen- 
eral preconception  arose.  It  certainly  did  not  come 
from  the  study  of  nature ;  for,  as  has  been  said,  the 
whole  scheme  of  nature,  so  far  as  we  understand  it, 
is  wholly  at  variance  with  such  an  idea.  Growth  is 
the  order  of  nature ;  and  although  as  yet  no  man  has 
been  able  to  discover  any  distinct  and  unquestionable 
traces  of  the  first  introduction  of  a  new  species  into 


284  ORIGIN   OF  THE   PRECONCEPTION. 

the  world,  yet  it  cannot  be  seriously  questioned  that 
the  theory  of  the  gradual  development  of  organic 
types  is  in  harmony  with  all  that  we  know  of 
biology. 

Nor  does  it  appear  probable  that  the  preconception 
came  from  the  Hebrew  Scriptures ;  for  although  in 
Genesis  it  is  distinctly  declared  that  all  things  were 
created  by  Jehovah,  the  great  "  I  Am,"  the  mode  of 
creation  is  described  in  such  obviously  figurative  lan- 
guage that  no  difficulty  has  been  found  in  reconciling 
it  with  any  result  of  science  when  once  clearly  estab- 
lished. Nevertheless,  it  is  very  generally  assumed 
that  a  creation  "  ex  nihilo  "  at  a  definite  moment  of 
time  is  expressly  declared  in  the  Bible,  and  on  this 
basis  it  is  constantly  urged,  in  answer  to  the  appar- 
ently irreconcilable  evidence  of  science,  that  the 
Almighty  could  instantly  call  a  universe  into  being 
out  of  nothing  if  He  chose.  Granting  a  clear  revela- 
tion, such  a  plea  might  be  relevant.  But  there  is  no 
such  clear  revelation ;  for  admitting  whatever  author- 
ity the  most  extreme  literalist  may  claim  for  the 
Pentateuch,  it  must  be  conceded  that  the  language 
of  these  early  books  admits  of  the  most  diverse  inter- 
pretations ;  and  the  mode  of  creation  still  remains  an 
open  question  for  scientific  investigation.  The  ques- 
tion is  not  how  to  reconcile  observation  and  revela- 
tion, but  to  find  out  as  far  as  possible  what  the  facts 
really  were. 

If,  then,  the  preconception  cannot  be  traced  either 
to  a  distinct  revelation,  or  to  the  observation  of  na- 
ture, must  it  not  result  from  the  normal  action  of  the 
human  mind  under  its  limitations?     In   all   human 


god's  creation  not  as  man's  creation.    285 

relations  creation,  whether  in  art,  in  literature,  or  in 
science,  implies  effort,  often  long-continued  effort, 
which  taxes  all  the  strength  and  all  the  perseverance 
that  the  most  gifted  men  can  command.  There  are 
obstacles  to  be  overcome,  and  there  is  a  conscious- 
ness of  weakness  and  inefficiency,  which  ever  reminds 
us  of  our  limited  powers.  Moreover,  at  most  our 
creation  consists  in  transforming  old  materials  into 
new  shapes.  The  potter  moulds  the  clay ;  the  sculp- 
tor chisels  the  marble,  and  both  clothe  with  beauty 
the  rude  materials  on  which  they  work ;  but  all  the 
while  they  are  painfully  conscious  of  the  limitations 
which  the  material  imposes  on  their  art.  It  is  nat- 
ural, therefore,  to  think  of  the  Almighty  as  a  power 
before  which  all  obstacles  yield  without  effort,  and 
which  can  call  order  and  beauty  not  only  out  of  chaos 
but  out  of  nothing.  There  is,  however,  an  illusion 
which  vitiates  this  inference;  and  the  old  apho- 
rism "  Ex  nihilo  nihil  fit "  is  much  nearer  the  truth. 
The  error  consists  in  overlooking  the  limitations  of 
time  by  which  we  are  circumscribed,  but  which  can- 
not bound  the  Creator.  Our  times  are  in  His  hands; 
but  God  himself  does  not  work  in  time.  "  God  work- 
eth  hitherto  and  I  work,"  said  the  Saviour ;  but  He 
worketh  not  as  man  worketh.  "  He  seeth  the  end 
from  the  beginning,  and  looketh  under  the  whole 
heavens ;  "  and  what  to  us  appear  as  consecutive  and 
consequent  are  to  Him  parts  of  a  plan  whose  pur- 
poses will  be  fully  revealed  only  when  time  shall  be 
no  more. 

The  view,  therefore,  that  a  theory  of  creation  by 
slow  development  derogates  from  the  attributes  of 


286  "  ETERNAL   GENERATION." 

the  Almighty  is  a  pure  illusion  resulting  from  our 
limitations.  To  Him  who  inhabiteth  eternity  pur- 
poses are  valued,  not  as  they  seem  to  ripen  fast  or 
slowly  to  us,  but  according  to  their  beneficent  de- 
sign. God,  who  is  ever  present  throughout  all  time 
both  to  will  and  to  do  of  His  good  pleasure,  compre- 
hends our  temporal  relations  in  His  all-embracing 
Providence,  and  adopts  methods  in  view  of  the  uni- 
versal, and  not  solely  of  a  temporal  good. 

In  all  material  relations  we  have  every  reason  to 
believe  that  the  knowledge  we  have  acquired  is  accu- 
rate and  trustworthy ;  but  in  speculating  about  spirit- 
ual relations,  we  must  always  remember  that  we  are 
liable  to  be  deceived  by  the  aberrations  of  our  mate- 
rial vision;  and  we  cannot  safely  build  a  theory  of 
the  universe  on  such  treacherous  foundations  as  our 
preconceptions  of  the  methods  of  the  Divine  govern- 
ment can  alone  furnish. 

The  conception  of  the  creative  power  as  acting 
through  an  indefinite  time,  or  rather  as  independent 
of  time,  was  familiar  to  Origen  and  the  other  Nicene 
fathers,  and  was  embodied  by  them  in  the  famous 
doctrine  of  the  "  Eternal  Generation,"  which,  although 
usually  limited  to  the  second  person  of  the  Trinity, 
was  by  Origen,  at  least,  extended  to  the  material 
creation. 

The  recognition  of  this  doctrine  as  applicable  in 
some  limited  measure  to  the  genesis  of  nature  would 
tend  very  greatly  to  reconcile  the  systems  of  theology 
with  the  systems  of  science.  For  if  the  theologian 
accepts  the  eternal  generation  of  the  Son  as  one  of 
the  most  fundamental  of  his  tenets,  how  can  he  con- 


ALL   KNOWLEDGE   IN   HARMONY.  287 

sistently  find  fault  with  the  analogous  doctrine  of 
science  which  involves  a  similar  idea? 

We  do  not  advance  the  doctrine  of  the  eternal  gen- 
eration of  matter  as  positive  knowledge,  or  even  as 
a  legitimate  inference  of  science ;  but  we  do  claim 
that  it  is  a  possible  inference  from  the  observed  facts 
of  nature,  and  that  it  is  in  entire  harmony  with  the 
most  profound  dogmas  of  theology. 

Such  speculations  may  have  little  value  towards 
establishing  truth  ;  but  they  at  least  show  how  foolish 
it  is  to  set  theological  dogmas  in  opposition  to  sys- 
tems of  science.  All  real  knowledge  must  eventually 
be  found  to  be  in  harmony,  and  the  only  way  to  find 
truth  is  to  seek  it  with  untiring  effort,  and  to  keep 
the  mind  unbiassed  by  any  theories  during  the  search. 
The  path  is  difficult,  the  labor  exhausting,  and  with- 
out faith  in  eternal  verities  the  investigator  will  soon 
lose  heart,  and  abandon  the  search.  If,  however, 
with  singleness  of  purpose  the  student  keeps  the  one 
great  aim  in  view,  and  not  only  has  faith  in  truth 
but  the  courage  to  face  it  in  whatsoever  guise  it 
may  appear,  he  will  gather  strength  as  he  pro- 
ceeds ;  and,  although  his  vision  in  this  life  may  be 
restricted,  and  he  may  not  rid  himself  of  earthly 
clogs,  yet  in  the  end  he  will  at  least  be  satisfied 
that  throughout  the  universe  of  being  One  Mind 
ruleth  over  all. 

Moreover,  such  speculations  may  have  this  positive 
result  in  so  far  as  they  show  that  time  is  not  the 
measure  of  spiritual  being.  There  are  often  periods 
in  life  when  crowding  opportunities  demand  more 
time  than  we  have  to  give.     But  taking  life  as  a  whole 


288  MORE  LIFE. 


there  is  time  enough  for  all  we  are  able  to  accomplish, 
and  it  is  more  energy,  and  not  more  time,  that  we 
really  need :  — 

"  'T  is  life  of  which  our  nerves  are  scant ; 
More  life  and  fuller,  that  I  want." 


THE  TWO   SYSTEMS.  2#g 


LECTURE   X. 

THE   SYSTEMS   COMPARED,  — RELIGION   AND 
SCIENCE. 

TN  the  necessarily  imperfect  sketch  of  scientific 
■*■  methods  which  has  been  given  in  the  previous 
lectures,  my  main  purpose  has  doubtless  been  obvi- 
ous from  the  first;  and  I  think  it  must  have  clearly 
appeared  that  the  speculative  objections  to  Christian 
belief  which  are  so  confidently  set  forth  are  no 
greater  than  must  be  encountered  in  every  depart- 
ment of  abstract  thought,  and  are  inseparable  from 
our  material  relations.  The  close  resemblance  in  this 
particular  between  the  systems  of  science  and  the 
systems  of  religion  presents,  as  it  seems  to  me,  by 
far  the  most  cogent  of  the  evidences  of  natural  the- 
ology; and  after  examining  the  features  of  the  scien- 
tific systems  it  remains  to  bring  together  the  separate 
threads  of  the  discussion  and  present  the  opposite 
side  of  this  very  striking  analogy. 

I  enter,  however,  on  this  part  of  the  task  I  have 
undertaken  with  great  diffidence.  Thus  far  I  have 
been,  for  the  most  part,  on  my  own  ground ;  now  I 
pass  over  on  to  yours.  And  at  the  same  time  I  feel  I 
ought  to  change  positions,  and  in  this  distinguished 
school  of  theological  learning  to  seek  instruction,  and 
not  attempt  to  teach.      I    feel,  moreover,  that   my 


290  POSITION  TAKEN. 


education  in  great  measure  unfits  me  for  the  office 
which  I  temporarily  fill;  and  as  it  is  impossible  that 
I  should  see  the  subject  from  your  point  of  view,  I 
fear  that  I  may  weaken  the  force  of  my  argument 
by  overlooking  features  which  you  deem  important ; 
or  even  involuntarily  offend  by  ignoring  doctrines 
which  you  deem  essential.  While  I  feel  the  firmest 
assurance  of  the  underlying  truths  of  Christianity,  and 
the  deepest  respect  for  every  honest  conviction,  still 
I  must  confess  that  my  whole  education  has  made  it 
impossible  for  me  to  attach  the  same  importance  to 
details  of  doctrine,  or  forms  of  ceremonial,  as  do 
those  who  have  been  trained  in  a  different  school, 
though  I  would  not  by  any  hint  of  mine  wound  the 
sensitive  realist,  or  the  conscientious  ceremonialist. 
I  say  this  without  the  least  assumption  of  greater 
freedom,  or  suspicion  of  complacency,  —  freely  ac- 
knowledging that  the  judgment  of  those  who  minister 
to  spiritual  needs  is  much  better  established,  and  not 
questioning  that  their  spiritual  insight  is  far  deeper 
than  mine. 

In  my  own  province  of  thought  I  know  so  well 
how  an  exact  knowledge  of  relations  will  often  set 
aside  judgments  which  a  superficial  knowledge  might 
seem  to  justify,  that  I  am  fully  sensible  that  the  same 
principle  must  hold  in  other  departments  of  learning 
equally ;  and  I  therefore  offer  the  argument  I  have  to 
make  simply  as  a  suggestion,  —  feeling  sure  that  it 
will  receive  your  thoughtful  consideration,  and  be 
accepted  for  all  it  is  worth.  Nevertheless,  I  have 
thought  —  otherwise  I  should  not  be  here  —  that 
a    certain    advantage    might    arise    in    presenting    the 


THE  ARGUMENT   STATED.  29 1 


subject  from  a  point  of  view  different  from  that  in 
which  a  theological  student  is  accustomed  to  regard 
it;  and  that  the  opinions  of  a  student  of  science,  who 
had  given  much  thought  to  such  questions,  however 
crude  his  theology,  might  help  you  to  meet  similar 
questions  which  sooner  or  later  in  your  ministry  will 
be  forced  by  thoughtful  men  on  your  attention.  I 
may  overestimate  the  strength  of  my  argument,  —  for 
the  force  of  an  analogical  argument  depends  very 
greatly  on  the  previous  experience  of  those  to  whom 
it  appeals,  —  but  it  has  come  home  with  overpower- 
ing force  to  my  own  mind;  and  I  find  it  difficult  to 
conceive  how  any  one  who  has  felt  the  bewilderment 
of  scientific  uncertainty,  as  well  as  of  religious  doubt, 
can  resist  its  cogency.  Take  out  the  elements  of 
feeling,  affection,  and  faith,  and  the  last  is  to  me  no 
more  oppressive  than  the  first. 

The  argument  itself  may  be  stated  in  a  few  words. 
As  there  are  systems  of  science,  so  there  are  systems 
of  religion  ;  and  among  these,  one  both  intellectually 
and  morally  so  far  in  advance  of  the  others  that 
it  alone  claims  the  consideration  of  educated  men. 
Regard  now  the  Christian  religion  simply  as  an 
external  fact,  as  an  existing  spiritual,  moral,  or  in- 
tellectual force,  independently  of  all  supernatural 
sanctions,  or  superhuman  obligations,  and  all  must 
admit  that  it  is  the  greatest  power  in  the  world. 
However  originating,  or  however  appointed,  there  is 
no  power  over  men's  minds  and  hearts  which  can 
for  one  moment  be  compared  with  it.  Throughout 
Christian  lands  this  power  is  everywhere  pervasive, 
and   even  in  lands  not  recognized   as  Christian  its 


292  THE   ARGUMENT   STATED. 

indirect  influence  has  softened  the  asperities  of  bar- 
barism, and  mitigated  the  cruelties  of  savage  life. 

Compare,  in  its  mere  external  or  intellectual  as- 
pects, Christianity  as  a  system  with  gravitation. 

As  the  way  was  prepared  for  Newton,  so  was  the  way 
prepared,  and  in  a  most  remarkable  manner,  for  the 
Founder  of  Christianity.  For  centuries  before  His 
coming  all  that  was  purest  and  noblest  in  the  world's 
thought  was  leading  up  to  the  expected  Messiah. 
Then  as  the  greatest  advance  ever  made  in  the 
knowledge  of  material  things  came  by  one  man, 
who  greatly  raised  the  level  of  scientific  thought,  so 
Christianity  came  like  a  great  induction  of  spiritual 
truth,  which  so  greatly  raised  the  level  of  spiritual 
thought  that  after  nearly  two  thousand  years  the 
Christian  world  does  not  yet  appreciate  the  elevation 
that  was  reached. 

As  modern  science  dates  from  Newton,  so  all  that 
is  noblest  and  best  in  man,  all  that  is  pure  and  lovely 
in  life,  all  unselfish  morality,  all  heroic  chivalry,  all 
holy  charity,  is  dated  Anno  Domini. 

The  Founder  of  Christianity  was  no  mythological 
hero ;  but,  whatever  views  we  may  entertain  of  his 
nature,  he  was  in  form  and  likeness  a  man,  living  at 
one  of  the  best  known  epochs  of  the  world's  history ; 
and  every  account  of  his  character  is  in  perfect  har- 
mony with  his  elevated  doctrines  and  momentous 
declarations. 

That  doctrine  and  those  declarations  present  diffi- 
culties of  conception.  We  cannot  reconcile  them 
with  our  experience  of  natural  relations;  and  in  the 
same  way  we  cannot  reconcile  the  system  of  gravi- 


THE   ARGUMENT   STATED.  293 


tation  with  our  knowledge  of  the  mode  of  action  of 
the  other  forces  of  nature. 

While,  however,  there  are  these  difficulties  of  con- 
ception, the  practical  application  of  Christian  doc- 
trine as  a  rule  of  life,  like  the  use  of  the  principle  of 
universal  gravitation  in  astronomical  computations,  is 
perfectly  simple  and  definite.  Indeed,  Christianity 
was  revealed  as  a  life,  and  has  been  handed  down  to 
us  pure  and  undenled  in  the  lives  of  its  disciples. 

Like  systems  of  science,  Christianity  deals  with 
symbols,  which  are  obviously  the  signs  of  realities 
in  their  essence  incomprehensible  by  man ;  and  even 
if —  as  does  at  times  happen  in  both  cases  — the  sign 
is  mistaken  for  the  substance,  still  such  symbols  are 
of  the  very  greatest  value  in  aiding  the  imagination 
and  guiding  the  thought. 

Newton  so  greatly  raised  the  level  of  astronomical 
conceptions  that  since  his  time  astronomers  have 
been  fully  occupied  in  deducing  the  consequences  of 
his  great  induction ;  and  so,  since  the  Christian  ages 
began,  apostles,  saints,  and  fathers,  with  lowly  and 
learned  men  of  every  name  and  calling,  have  been 
diligently  unfolding  the  beauties,  the  marvels,  and 
the  glories  of  the  truth  that  was  then  revealed.  No 
wonder  that  the  interpretations  did  not  always  agree, 
that  bitter  controversies  arose,  and  that  men  profess- 
ing the  faith  used  power  and  influence  as  instruments 
of  oppression  and  persecution  ;  for  the  same  sad  feat- 
ures have  disgraced  the  history  of  science,  without 
the  excuse  of  intense  feeling  to  inflame  passion  or  of 
blind  fanaticism  to  obscure  reason.  But  as  in  spite 
of  follies  and  quarrels  astronomy  has  grown  to  be  a 


294  THE   ARGUMENT   STATED. 


noble  science,  worthy  of  the  most  gifted  human  in- 
telligence, so  in  an  immeasurably  greater  degree  the 
Christian  Church  through  weakness  has  been  made 
strong,  and  has  become  a  holy  temple  in  which  the 
loftiest  aspiration  finds  satisfaction,  the  purest  affec- 
tion repose,  and  unsullied  charity  its  full  reward. 

Lastly,  as  the  system  of  gravitation  has  been  tested 
and  ratified  by  the  complete  accordance  of  natural 
phenomena  with  the  deductions  that  it  involved,  so 
has  a  most  commanding  seal  been  set  on  Christianity 
by  the  entire  harmony  of  the  system  with  the  spir- 
itual needs  of  man.  It  is  in  that  harmony  that  all 
its  strength  lies.  It  has  been  tested  by  the  most 
varied  experience.  The  blood  of  the  martyrs  has 
been  the  seed  of  the  Church ;  and  the  attestation  of 
the  great  army  of  its  confessors  rolls  down  the  Chris- 
tian centuries  with  ever  louder  shouts  of  rejoicing 
and  songs  of  thanksgiving  and  praise.1 

While  thus  wonderfully  adapted  to  man's  spiritual 
needs,  so  just  in  proportion  as  our  knowledge  be- 
comes enlarged,  and  our  insight  deepened,  is  Chris- 
tianity found  to  be  in  harmony  with  all  truth.  The 
most  gifted  minds  and  profoundest  scholars  the  world 
has  known  have  not  only  confessed  Christ  before 
men,  and  acknowledged  Him  to  be  the  Lord,  but  have 
also  testified  that  increasing  acquirements  and  widen- 

1  This  test  of  experience,  so  clearly  recognized  in  science,  is 
also  accepted  in  theology ;  and  even  Roman  Catholic  doctors 
admit  that  the  decrees  of  Councils  must  be  accepted  by  the  pub- 
lic mind  of  the  Church  before  they  can  be  declared  the  voice  of 
God.  As  early  as  the  fifth  century  Vincentius  Lirinensis  laid 
down  as  the  test  of  authority:  "Quod  semper,  quod  ubique, 
quod  ab  omnibus  creditum  est." 


CHRISTIANITY  A   FACT   OF  NATURE.  295 

ing  vision  brought  an  ever  deeper  conviction  of  His 
truth. 

If,  then,  man  can  in  any  case  rely  on  his  experi- 
ence as  a  test  of  truth ;  if  harmony  with  nature  is 
any  evidence  of  participation  in  the  scheme  of  na- 
ture ;  if  this  world  is  not  wholly  a  phantom  and  a 
deceit;  if  all  knowledge  is  not  equally  delusive,  —  then 
the  essentials  of  Christianity  must  be  true.  Such  is 
the  argument.  You  must  have  anticipated  it  as  I 
traced  out  the  features  of  scientific  systems ;  and  I 
have  only  to  add,  before  concluding  this  course  of 
lectures,  some  connected  thoughts  which  may  serve 
to  enforce  or  illustrate  special  points  of  this  strik- 
ingly close  analogy. 

Remember,  in  the  first  place,  that  we  are  here 
treating  Christianity  as  a  fact  of  nature,  as  an  exist- 
ing system  of  religious  truth,  on  the  same  plane  as 
any  other  system  of  knowledge ;  and  from  this  point 
of  view  only  do  we  compare  it  with  systems  of  sci- 
ence, like  the  system  of  gravitation.  We  all  believe 
that  Christianity  has  other  sanctions  and  attestations  ; 
but  in  a  question  of  Natural  Theology  we  leave  all 
this  evidence  on  one  side,  and  deal  with  Christianity 
only  as  an  external  fact  of  nature,  as  an  historical 
phase  in  the  development  of  humanity,  as  a  system 
of  morals,  as  a  system  of  philosophy,  or  as  a  guiding 
and  directing  motive  which  controls  large  masses  of 
mankind.  I  trust  that  I  am  not  misunderstood; 
although  there  is  an  obvious  rhetorical  difficulty  in 
dealing  with  the  subject  in  this  way.  My  language 
might  very  easily  be  misconstrued,  although  I  have 
earnestly  endeavored  to  avoid  the  occasion.     No  one 


296  CHRISTIANITY   A   FACT  OF  NATURE. 

who  has  deep  religious  feeling  can  associate  even  in 
the  most  indirect  way  Christianity  with  a  system  of 
science;  or  the  Founder  of  Christianity  with  the 
originator  of  such  a  system,  however  great  and 
worthy,  without  feeling  the  incongruity  which  the 
comparison  involves ;  and  it  is  difficult  to  find  lan- 
guage which  shall  convey  my  meaning  without  a 
suggestion  of  irreverence.  You  will,  I  am  sure,  ap- 
preciate the  difficulty  and  pardon  any  infelicity. 

We  are  dealing  solely  with  the  evidence  of  nature, 
and  we  must  treat  Christianity  as  a  part  of  nature, 
just  as  gravitation  is  a  part  of  nature,  if  we  would 
estimate  the  value  of  the  evidence  which  nature  alone 
can  give  apart  from  all  other  sanctions.  Of  course 
other  evidences  have  their  due  place,  and  to  most 
minds  have  such  a  paramount  authority  as  to  wholly 
hush  the  feeble  voice  of  nature.  But  I  am  here  to 
show  you,  as  far  as  I  am  able,  how  forcible  the  tes- 
timony of  nature  is  by  itself,  apart  from  any  super- 
natural credentials ;  and  I  affirm  that  Christianity  as 
an  external  fact  is  a  part  of  this  evidence.  Chris- 
tianity is  a  definite  force  in  the  world,  and  is  as 
essential  a  factor  in  the  development  of  humanity, 
as  steam-power,  electricity,  or  natural  selection. 
The  supernatural  evidence  of  Christianity  is  wholly 
additional  to  the  sanctions  we  urge  ;  and  the  former 
is  rendered  vastly  more  credible  and  persuasive  by 
the  evidence  of  nature.  If  you  can  remove  the  ante- 
cedent presumption  against  the  miraculous,  you 
place  at  once  the  overwhelming  historical  evidences 
of  Christianity  on  the  same  basis  as  all  other  his- 
torical testimony;   and  how  can  you  accomplish  this 


THE   ULTIMATE  TEST   OF  TRUTH.  297 

so  effectually  as  by  showing  that  the  resulting  system 
is  in  entire  harmony  with  what  are  always  regarded 
as  earth-born  systems? 

I  must,  however,  myself  protest  against  the  last 
term,  while  using  it  to  point  a  distinction.  I  believe 
most  firmly  that  all  truth  is  one  and  inseparable, 
and  that  there  is  no  real  distinction  between  heaven- 
born  truth  and  earth-born  truth.  I  believe  that  in 
the  strict  sense  of  the  term,  gravitation  was  as  much 
a  revelation  to  man  as  Christianity.  I  cannot,  there- 
fore, call  one  human  and  the  other  divine.  Grant 
the  widest  difference  between  the  modes  by  which 
the  revelations  were  communicated.  Grant  that  the 
very  diverse  nature  of  the  revelations  required  this 
difference ;  yet  in  either  case  the  truth  is  God's 
truth ;  and  in  the  last  analysis,  the  ultimate  test  of 
all  truth  must  be  its  universal  and  perfect  harmony. 
To  me  the  most  weighty  evidence  of  Christianity  is 
its  supreme  naturalness ;  that  intensely  human  life  in 
the  past,  that  Holy  Church  ever  since,  in  perfect 
harmony  with  all  my  purest  affections  and  loftiest 
aspirations,  is  the  strongest  assurance  of  truth,  —  and 
truth  is  always  and  everywhere  divine. 

Again,  Christianity  as  a  fact  of  nature  involves  all 
prior  questions  as  to  the  personality  of  the  Godhead, 
or  the  attributes  of  Deity.  We  have  no  occasion  to 
go  back  to  questions  of  design,  or  plan  in  nature. 
We  deal  with  the  most  conspicuous  design,  the  most 
wonderful  plan;  and  if  these  are  shown  to  be  of  a 
piece  with  the  rest  of  nature,  why  need  we  further 
testimony?  In  the  first  lecture  of  this  course,  we 
endeavored  to  show  that  all  arguments  from  adapta- 


298  ADAPTATION  TO   MAN'S   WANTS. 

tion  or  from  general  plan  were  inductions  based  on 
analogy;  and  that  like  other  inductions  their  force 
depended  on  the  fulness  with  which  they  harmonized 
the  facts  of  nature.  We  claim  for  our  present  argu- 
ment the  same  validity ;  and  if  the  claim  is  allowed, 
the  argument  has  a  far  greater  range  than  any  pre- 
vious argument  of  natural  theology;  for  it  secures 
all  that  Christianity,  as  an  external  fact  of  nature, 
can  be  justly  claimed  to  include.  And  looking  at 
the  question  in  its  simplest  aspect,  why  is  not  the 
adaptation  of  Christianity  to  man's  spiritual  wants  as 
direct  an  evidence  of  design  as  the  adaptation  of 
the  eye  to  seeing,  or  the  lungs  to  breathing?  —  and 
regarding  the  plan  of  redemption  simply  as  it  was 
first  exhibited  by  the  life  and  death  of  Christ,  and  as 
it  has  been  exemplified  in  the  lives  and  deaths  of 
saints  and  martyrs  ever  since,  as  conclusive  an  evi- 
dence of  intelligence  as  the  plan  of  the  vertebrate 
skeleton,  or  the  spiral  distribution  of  leaves  on  the 
stems  of  plants? 

We  have  in  the  most  positive  manner  affirmed 
that  inductions  based  on  analogy  or  otherwise  are 
not,  and  from  the  nature  of  the  case  cannot  be,  dem- 
onstrations; and  have  shown  that  they  may  offer 
every  degree  of  conclusiveness  depending  on  their 
agreement  with  the  phenomena  of  nature.  We  could 
have  no  more  perfect  accordance  than  Christianity 
offers.  But  however  conclusive  such  evidence,  there 
is  always  room  for  speculative  doubt;  and  we  freely 
admit  that  our  argument  is  not  a  proof,  but  it  affords 
all  the  certainty  we  can  have  in  natural  theology. 

As  I  have  before  said,  it  is  a  striking  fact  in  regard 


THE   WAY   WAS   PREPARED.  299 

to  all  scientific  inductions  that  they  never  come  to 
fruition  until  the  time  is  ripe.  If  premature,  they 
fall  on  barren  soil,  and  the  numberless  anticipations 
of  genius  are  well-known  illustrations  of  this  truth. 
And  when  we  consider  the  obvious  law  of  progres- 
sion which  the  development  of  knowledge  obeys,  we 
are  forced  to  recognize  that  individual  men,  however 
great  their  genius,  are  not  essential  to  the  result. 
Like  the  prophets  of  old,  they  are  interpreters  of  a 
preordained  purpose.  No  one  can  question  that  the 
law  of  gravitation  would  have  been  discovered  within 
half  a  century,  if  Newton  had  not  lived ;  and,  great  as 
his  influence  has  been,  and  greatly  as  he  hastened 
the  progress  at  the  time,  astronomy  would  certainly 
have  been  as  far  advanced  to-day  if  the  work  had 
been  left  for  other  hands.  Since  the  time  of  Hippar- 
chus  the  way  had  been  preparing  for  the  great  in- 
duction ;  and  Isaac  Newton  was  the  name  given  to 
the  faithful  and  gifted  servant  who  was  born  into 
the  world  when  the  time  was  ripe. 

Again,  how  striking  the  analogy  with  the  coming  of 
Christianity !  Here  also  the  way  was  prepared.  "  But 
when  the  fulness  of  the  time  was  come  God  sent  forth 
his  Son,  made  of  a  woman,  made  under  the  law ;  " 
and  although  the  messenger  was  the  Divine  Son,  and 
the  message  was  the  redemption  of  man,  yet  the  gos- 
pel came  in  the  same  simple  naturalness  with  which 
every  great  truth  has  come  to  the  world.  Before 
John  came  crying  in  the  wilderness,  how  long,  how 
tedious,  and  how  devious,  had  been  the  way,  how 
halting  the  progress ;  yet  from  time  to  time  seer  and 
prophet  had  caught  glimpses  of  the  coming  truth  as 


300  THE   COMING. 


they  diligently  toiled  in  the  vineyard,  and  sought  to 
make  ready  for  the  vintage  of  the  Lord. 

As  I  ponder  this  sublime  history  I  cannot  resist 
the  impression  that  this  conformity  to  natural  methods 
is  an  irresistible  evidence  of  genuineness  which  we 
cannot  afford  to  overlook.  God  introduced  Chris- 
tianity into  the  world  by  the  same  methods  by  which 
He  has  opened  to  us  all  knowledge,  —  in  order  that 
He  should  not  confuse  the  understanding,  or  confound 
the  intelligence,  of  His  creatures  ;  and  thus  it  is  that 
our  expanding  science  becomes  to  us  on  a  lower 
scale  a  type  and  similitude  of  the  methods  of  Divine 
revelation ;  and  the  certitude  of  the  one  gives  us  a 
confident  assurance  of  the  certitude  of  the  other. 

It  was  because  I  wished  to  set  forth  this  analogy 
in  a  strong  light  that  I  dwelt  at  some  length  on  the 
prelude  to  the  discoveries  of  Newton,  —  in  order  that 
you  might  see  that  his  way  was  prepared  by  methods 
not  always  direct,  and  by  servants  not  always  worthy, 
and  yet  that  all  conspired  to  ensure  the  final  result ; 
and  that  thus  you  yourselves  might  draw  out  the  anal- 
ogy with  a  power  which  I  am  unable  to  command. 

In  entire  harmony  with  the  perfect  naturalness  of 
the  whole  dispensation  was  the  coming  itself.  It  was 
not  in  an  obscure  period  of  human  history,  or  in  a 
remote  corner  of  the  earth ;  but  in  the  midst  of  the 
Roman  Empire,  and  during  the  Augustan  age  of  the 
ancient  civilization.  The  coming  was  not  heralded 
by  signs  and  portents  which  inspired  awe  and  com- 
manded attention  ;  but  in  all  the  simplicity  of  child- 
hood, and  in  all  the  naturalness  of  growth.  What  a 
lesson   is   there    in   the  simple  statement  that  "  the 


GRADUAL  UNFOLDING.  30 1 


child  grew,  and  waxed  strong  in  spirit."  And  so  un- 
obtrusive and  unobserved  was  this  growth,  except 
by  a  few  humble  peasants,  that  when  the  glory  of  His 
mature  powers  broke  upon  the  Jewish  world  it  ex- 
cited the  wondering  remark,  "  Whence  hath  this  man 
letters,  having  never  learned?" 

In  respect  only  to  this  natural  growth,  but  as  a 
further  incidental  illustration  of  the  fact  that  the  most 
glorious  of  all  advents  came  to  the  world  with  entire 
conformity  to  natural  methods,  allow  me  in  all  rever- 
ence again  to  call  your  attention  to  the  striking  cir- 
cumstance in  the  life  of  Newton,  upon  which  I  have 
before  dwelt, — that  we  find  him,  while  still  a  college- 
student,  in  possession  of  mathematical  power,  and  of 
a  new  calculus,  not  only  far  in  advance  of  his  teachers 
but  also  of  his  age.  The  advent  of  new  truth  has 
always  been  by  the  same  gradual  unfolding  ;  and  is 
there  not  the  strongest  antecedent  presumption  that 
He  of  whose  fulness  we  all  partake  should  in  His 
mediatorial  office  conform  to  the  same  methods  He 
had  Himself  ordained?  And  is  not  the  harmony  of 
the  result  with  this  antecedent  presumption  the 
strongest  possible  evidence  of  genuineness?  Would 
man's  invention  in  a  pre-Christian  age  ever  have 
conceived  of  such  a  method  or  pictured  such  a 
likeness? 

The  feature  which  above  all  things  else  is  most 
striking  in  a  great  induction  is  that  such  an  advent 
raises  the  level  of  human  thought.  Therefore  such 
inductions  mark  epochs  in  science.  Astronomy 
points  back  to  Newton;  and  no  one  can  question 
that  for  years  to  come  natural  history  will  point  back 


302  ANCIENT  AND  MODERN   CIVILIZATION. 

to  Darwin.  How  is  it  with  religious  thought?  The 
comparison  may  seem  almost  irreverent;  and  yet  it  is 
highly  instructive.  Looking  at  Christian  institutions 
simply  as  outward  facts,  without  regard  to  sanctions, 
dogmas,  doctrine,  or  creeds  of  any  kind,  what  do  we 
see?  No  less  than  this :  that  everything  in  the  world 
which  is  loftiest  and  profoundest  in  thought,  which 
is  most  ennobling  and  heroic  in  character,  which  is 
bravest  and  most  unselfish  in  action,  which  is  purest 
and  loveliest  in  art,  which  is  most  consoling  or  hope- 
ful in  philosophy,  and  above  all  this,  every  form  of 
beneficent  charity,  every  movement  for  the  amelior- 
ation of  mankind,  every  influence  which  sanctifies 
family  ties,  dates  from  one  conspicuous  and  definite 
epoch  of  the  world's  history  from  which  civilized 
men  began  to  count  anew  the  revolving  years. 

I  certainly  need  not  in  this  place  attempt  to  draw 
a  parallel  between  the  ancient  and  the  modern  civili- 
zation, to  show  how  great  a  change  was  wrought,  and 
how  great  an  elevation  was  reached  in  one  short  life. 
But  if  in  the  interest  of  natural  theology  I  can  induce 
you  to  look  at  the  subject  from  my  point  of  view, 
and  for  the  sake  of  argument  to  consider  the  claims 
of  Christianity  as  simply  an  external  feature  in  human 
society,  I  hope  I  may  render  a  real  service  by  giving 
you  the  command  of  a  very  powerful  argument  which 
can  be  pressed,  not  only  without  compromising  or 
invalidating  any  supernatural  evidences,  but  on  the 
contrary,  which  will  furnish  a  secure  basis  on  which 
such  claims  can  be  established.  It  must  be  that  a 
system  which  is  so  obviously  a  part  of  nature  has  the 
same  authenticity  as  the  rest  of  nature;    and  then 


NATURE   AND   THE   SUPERNATURAL.  303 

comes  home  with  redoubled  force  the  old  argument 
that  men  unaided  could  not  have  raised  themselves 
by  one  leap  to  such  an  elevation. 

Even  in  regard  to  scientific  discoveries  it  inspires 
confidence  to  know  that  the  investigator  was  in  full 
relations  with  his  subject,  and  in  all  respects  equal  to 
his  work;  and  we  have  shown  how  conspicuously 
this  was  true  in  the  case  of  Newton.  But  who  can 
"  speak  the  matchless  worth "  of  the  Founder  of 
Christianity?  Certainly  not  a  layman  in  this  place. 
It  is  to  be  your  great  privilege  to  rehearse  this  story ; 
and,  as  told  by  your  lips,  in  simplicity  and  power, 
may  it  bring  consolation,  comfort,  and  conviction  to 
many  a  weary  and  troubled  soul.  In  seeking  to 
make  evident  that  "  Nature  and  the  Supernatural," 
are  "The  one  System  of  God,"  a  most  gifted  and 
spiritually  minded  American  clergyman,  the  late 
Horace  Bushnell,  has  sounded  forth  the  glories  of 
that  wondrous  tale  "  in  notes  almost  divine;  "  and  in 
following  his  chaste,  beautiful,  and  effective  presen- 
tation of  the  character  of  Christ,  the  one  feature  that 
most  impresses  the  reader  is  its  supreme  naturalness. 
The  consciousness  of  power  is  all  there ;  the  mystery 
of  personality  is  all  there;  the  terror  of  justice  is  all 
there ;  the  avvfulness  of  sacrifice  is  all  there.  But  it 
is  the  sweetness  of  affection,  the  tenderness  of  com- 
passion, the  earnestness  of  pity,  the  fervor  of  charity, 
the  ardor  of  zeal,  the  devotion  to  duty,  the  submission 
to  authority,  the  perfection  of  manhood,  which  rivets 
our  attention,  which  engages  our  sympathies,  which 
commands  our  reason. 

All  systems  of  science,  as  we  have  seen,  present 


304  DIFFICULTIES   OF   CONCEPTION. 

insuperable  difficulties  of  conception,  because  mate- 
rial relations  are  the  measure  of  our  experience  and 
therefore  the  measure  of  our  positive  knowledge. 
Can  we  expect  that  the  philosophy  of  religion  will 
be  more  intelligible?  And  the  more  we  study,  the 
more  plainly  it  will  appear  that  in  this  respect  also 
the  two  orders  of  truth  present  a  most  striking  anal- 
ogy;  and  that  in  either  case  the  difficulties  arise  from 
the  impossibility  on  our  part  of  picturing  to  the  mind 
any  relations  not  realized  in  our  own  experience  or 
in  that  of  our  fellow-men.  Even  in  regard  to  material 
relations  there  is  a  great  difference  among  educated 
men  in  the  power  of  realizing  unseen  conditions  ;  and 
to  rude,  unimaginative  folk  nothing  exists  beyond  the 
range  of  their  immediate  perceptions.  With  those 
whose  imaginative  faculties  have  been  most  cultivated, 
the  limit  of  power  is  soon  reached  ;  and  however 
much  the  philosopher  may  speculate  about  trans- 
mundane  realities,  and  however  firmly  he  may  believe 
in  them,  he  can  form  no  mental  images  of  such  beings 
that  are  not  painted  in  colors  of  clay.  Hence  it  is 
that  I  have  dwelt  so  fully  on  the  difficulties  of  con- 
ception which  the  fundamental  concepts  of  physical 
science  present, — in  order  that  you  might  appreciate 
how  very  close  is  the  analogy  which  I  am  endeavoring 
to  enforce. 

The  incongruities  and  apparent  inconsistencies 
which  the  systems  of  science  involve  do  not  invali- 
date their  essential  truth,  but  they  do  most  conclu- 
sively indicate  that  we  are  dealing  with  relations 
beyond  the  range  of  our  experience  ;  and  our  at- 
tempts to  represent  these  relations  to  our  minds  by 


NATURALNESS   OF  THE   GOSPEL.  305 

means  of  ethereal  media  or  assumed  attractions  re- 
semble the  play  of  children  with  their  dolls  and  toys. 

In  like  manner  it  is  no  objection  to  a  theological 
system  that  it  involves  much  that  is  incomprehensible 
and  seemingly  contradictory.  The  question  simply 
should  be,  Does  it  give  a  faithful  representation  of 
known  facts  and  relations?  and  if  so,  the  inconsis- 
tencies indicate  no  more  than  this,  that  it  deals 
with  forms  of  being  beyond  the  range  of  human 
experience. 

It  is  to  me  a  striking  evidence  of  the  truth,  as  well 
as  of  the  naturalness  of  the  gospel  narrative,  that 
throughout  there  should  be  such  an  accommodation 
to  the  necessary  limitations  of  human  intelligence. 
On  all  occasions  the  truth  is  presented  in  the  simplest 
material  imagery,  and  the  most  tender  regard  is  paid 
to  the  Marthas  and  Thomases  of  every  age,  to  whom 
seeing  could  give  to  belief  the  only  adequate  certi- 
tude ;  and  when  it  was  necessary  to  certify  to  eternal 
realities  and  to  arouse  men  from  their  material  leth- 
argy, how  unaffectedly  it  is  done  with  a  few  simple 
but  grand  sentences.  How  differently  it  would  have 
been,  how  differently  it  has  been,  with  every  human 
teacher  to  whom  has  been  opened  a  vision  of  things 
eternal.  How  irresistible  has  always  been  the  ten- 
dency of  the  human  mind,  however  enlightened,  to 
dwell  on  all  that  is  anomalous,  incongruous,  or  awe- 
inspiring,  in  the  situation  described.  We  find  this 
most  markedly  in  the  elder  dispensation.  We  find 
it  even  in  the  vision  of  the  Apocalypse.  And  is 
there  not  a  lesson  in  such  facts  which  we  may  well 
ponder? 


306  PARADOXES   OF   DOGMAS. 

In  teaching  physical  science  it  would  be  very  un- 
wise to  give  prominence  to  the  difficulties  of  concep- 
tion on  which  for  a  special  purpose  we  have  dwelt  in 
these  lectures.  These  are  real  difficulties,  and  must 
be  met  by  every  thoughtful  student  sooner  or  later ; 
but  they  have  no  practical  significance,  and  are 
wholly  ignored  in  the  every-day  work  of  the  labo- 
ratory. Of  course  no  feeling  is  here  involved,  as  in 
religious  questions ;  but  with  all  this  difference  is  it 
wise,  in  an  age  which  is  so  much  engrossed  with  ma- 
terial interests,  to  give  prominence  to  similar  difficul- 
ties of  theological  doctrine  that  have  as  little  bearing 
on  Christian  living?  Is  it  not  better  that  they  should 
be  ignored  than  become  hindrances  to  faith?  and 
does  not  all  experience  teach  that  a  faith  well- 
grounded  on  personal  experience  and  active  benevo- 
lence will  accept  any  doctrine  once  delivered  to  the 
saints  whose  holy  lives  it  seeks  to  imitate? 

Our  Puritan  forefathers  delighted  in  theological 
dialectics,  and  sought  to  exaggerate  rather  than  to 
reconcile  the  paradoxes  and  contradictions  of  dogmas. 
They  were  thoughtful  men  of  speculative  dispositions, 
whom  both  political  circumstances  and  sensitive  con- 
sciences had  debarred  from  the  intellectual  life  of  the 
world,  and  who  found  the  chief  exercise  of  their  in- 
telligence in  the  discussion  of  theological  dogmas. 
But  it  may  be  doubted  whether  this  at  times  morbid 
exercise  of  their  faculties  induced  any  more  humble 
and  loving  lives  than  those  of  many  a  devoted  saint 
who  never  so  much  as  heard  of  Foreknowledge  or 
Predestination. 

In  connection  with  the   difficulties  of  conception 


CONTINUITY  OF  LIFE.  307 

which  the  Christian  system  involves,  the  question  of 
the  Christian  miracles  at  once  suggests  itself;  but 
this  is  too  large  a  subject  to  be  discussed  here.  Two 
principles,  however,  which  we  have  sought  to  estab- 
lish, have  a  bearing  upon  the  matter.  The  first  is 
that,  with  certain  obvious  limitations,  there  can  be  no 
prodigy  in  nature  so  wonderful  that  it  may  not  be 
accepted  on  adequate  evidence;  and  the  second  is 
that  so  far  as  our  knowledge  extends  there  is  ample 
room  for  the  appearance  of  new  forces  in  the  chain 
of  causation.  Obviously  these  principles,  if  estab- 
lished, remove  in  very  great  measure  the  antecedent 
presumption  against  miracles,  and  leave  their  authen- 
ticity to  be  established  in  every  case  by  the  evidence 
alone.  In  weighing  evidence  men  will  be  guided  by 
the  self-evident  truth  that  it  is  more  probable  that  a 
witness  should  be  deceived  than  that  the  usual  order 
of  nature  should  be  altered ;  and  if  the  evidence  is  in 
question,  the  counter  presumption  thus  created  is 
overwhelming.  But  in  the  presence  of  well-attested 
fact  all  questions  of  probability  scatter  to  the  winds ; 
and  what  better  attestation  of  an  historical  fact  can 
you  have  than  continuity  of  life?  and  I  question  if 
any  one  who  has  fully  partaken  of  that  life  ever 
questioned  the  validity  of  the  evidence. 

Thus  the  continuous  life  of  the  Church  from  the 
beginning  becomes  the  most  convincing  evidence  of 
the  Resurrection,  that  of  all  Christ's  miracles  the  most 
vital  to  the  authority  and  influence  of  His  Church ; 
for  "  if  Christ  be  not  risen  then  is  our  preaching  vain, 
and  your  faith  is  also  vain."  Just  as  the  religion  of 
Mahomet,  as   a   power   in   history,  dates   from   the 


308  THE   RESURRECTION. 

Hegira,  and,  however  surprising  the  effects  ulti- 
mately produced  by  such  gross  materialism,  presents 
a  perfect  continuity  from  the  first,  each  step  of  the 
progress  being  natural  and  intelligible,  —  so  Chris- 
tianity, as  a  force  in  society,  dates  from  the  Resur- 
rection, and  shows  an  unbroken  line  of  sequences 
from  that  event.  Granted,  if  you  demand  it,  that  the 
Resurrection  was  a  condescension  to  the  conditions  of 
our  material  existence.  Explain  the  outward  aspects 
of  the  event  as  you  please.  Still  there  remains  the 
fact  of  history  that  something  occurred  at  that  time 
which  produced  conviction  on  the  minds  of  the  be- 
holders, and  to  which  the  origin  of  the  Christian 
Church  must  be  traced. 

The  high  morality  of  Christ's  teaching  cannot 
account  for  the  founding  of  such  a  church.  The 
Crucifixion  destroyed  all  hope  even  in  the  small 
band  of  followers  who  were  faithful  to  the  last ;  and 
without  some  remarkable  attestation,  Christ's  teach- 
ing would  have  produced  no  more  effect  on  the 
world  than  that  of  Socrates,  or  of  Plato,  even  if  the 
records  had  been  preserved.  Something  must  have 
occurred  which  changed  despondency  to  hope,  and 
which  inspired  the  disciples  with  courage  and  enthu- 
siasm. The  gospel  narrative  gives  an  explanation 
which  accounts  for  the  result.  The  wonderful  event 
which  had  been  predicted  took  place.  Man  could 
have  no  conviction  except  through  experience,  and 
the  experience  was  furnished. 

We  cannot  suspect  the  founders  of  Christianity  of 
deliberate  falsehood,  any  more  than  we  can  believe 
that  an  event  from  which  such  great  consequences 


THE  RESURRECTION.  309 

immediately  flowed  was  a  myth.  The  witnesses  must 
have  believed  that  they  saw  what  they  described. 
Explain  away  the  facts  as  you  please.  Regard  the 
phenomena  observed  as  purely  subjective  to  the 
minds  of  those  present,  and  the  outward  appearances 
as  delusive,  it  still  must  be  admitted  that  something 
occurred,  either  outwardly  or  inwardly,  which  pro- 
duced such  a  profound  impression  on  the  minds  of 
the  beholders  as  to  arouse  the  highest  enthusiasm, 
and  the  most  unselfish  devotion,  the  world  has  ever 
known ;  and  from  which  a  chain  of  consequences  has 
been  forged  link  by  link  until  all  that  is  best  and 
noblest  of  the  human  race  has  been  enchained  in  its 
bonds  of  love. 

Herein  lies  the  great  wonder.  The  miracle  was  not 
wrought  for  us.  Thank  God  !  we  cannot  investigate 
the  circumstances  now,  or  analyze  all  the  material 
imagery  that  was  accessory  to  that  solemn  scene. 
But  of  this  at  least  we  may  be  sure :  at  that  time  a 
new  motive  came  into  operation  which  changed  the 
whole  order  of  society,  and  to  this  time  history  points 
continuously  back,  as  it  does  to  Caesar  crossing  the 
Rubicon,  or  to  Luther  nailing  his  theses  to  the  door 
of  the  Schlosskirche  at  Wittenberg.  If  there  be  such 
a  thing  as  order  in  the  evolution  of  nature  this  event 
was  a  part  of  that  order.  If  there  be  an  intelligent 
Ruler  of  the  world  this  event  was  ordained  by  Him ; 
and  whether  He  worked  through  methods  intelligible 
to  us,  or  by  means  past  our  finding  out,  and  which 
with  our  limited  knowledge  and  experience  we  call 
supernatural,  the  event  was  no  less  miraculous  in  its 
occurrence,  no  less  wonderful  in  its  result. 


310  THE   SYMBOLISM   OF   CHRISTIANITY. 

Turning  now  to  the  practical  working  of  the  Chris- 
tian system,  how  simple  are  the  principles  of  action, 
how  plain  the  duties ;  and  what  Christian  mother 
watching  over  her  sick  child,  what  aged  saint  nearing 
his  rest,  or  what  soldier  of  Christ  in  the  midst  of  the 
conflict  were  ever  troubled  by  difficulties  of  concep- 
tion?    Our  analogy  here  again  is  perfect. 

I  hope  further  that  the  analogy  of  the  symbolism 
of  science  may  aid  us  to  a  better  understanding  of 
the  purport  of  the  symbolism  of  Christianity.  We 
have  endeavored  to  show  that  the  symbols  in 
chemistry  were  something  more  than  mere  conven- 
tionalism ;  that  although  absurd  and  grotesque  if 
regarded  as  the  exact  patterns  of  realities,  they  were 
obviously  the  signs  of  an  underlying  truth  as  yet 
only  dimly  apprehended.  How  characteristic  this  is 
also  of  all  the  legitimate  symbols  of  Christianity,  in- 
cluding under  this  term  much  of  the  imagery  both  of 
the  Old  and  of  the  New  Testaments.  These  are  pro- 
fessedly types,  not  likenesses  of  spiritual  being;  but 
like  the  symbols  of  science,  they  are  aids  to  the  im- 
agination, they  give  definiteness  to  thought,  they 
give  substance  to  things  unseen.  Such  types,  how- 
ever, must  resemble  in  certain  features  their  origi- 
nal, inasmuch  as  they  form  a  safe  basis  of  inference, 
and,  like  the  symbols  of  science,  guide  the  mind  to 
the  discovery  of  truth.  Like  the  ladder  seen  in  vis- 
ion by  the  patriarch  at  Bethel,  they  rest  on  earth, 
but  they  lead  upwards  to  where  the  material  blends 
with  the  spiritual  in  the  effulgence  of  Divine  glory. 
On  the  other  hand,  as  the  conventional  forms  of 
science  often  acquire  an  undue  prominence,  and  be- 


GRADUAL  UNFOLDING.  3  1 1 

come  invested  with  an  imaginary  concreteness  in  the 
thoughts  of  those  who  are  constantly  occupied  there- 
with, so  the  symbolism  of  Christianity  is  also  too 
frequently  materialized,  and  the  spirit  that  giveth 
life  completely  hidden  by  the  letter  that  killeth. 

In  all  great  scientific  inductions  which  have  per- 
manently raised  the  level  of  human  knowledge,  the 
advantage  gained  has  never  been  appreciated  at  the 
time,  and  it  has  been  the  work  of  years  to  develop 
the  consequences  of  a  single  lofty  intellectual  con- 
ception. Here  again  the  parallelism  is  most  striking 
with  the  Christian  revelation.  How  faintly  did  the 
earlier  disciples  comprehend  the  work  of  their  Mas- 
ter; and,  as  century  after  century  has  passed  since, 
how  slowly  has  the  world  come  to  a  realization  of  the 
truth ;  and  in  proportion  as  man  has  become  enlight- 
ened, how  steadily  has  the  scope  of  the  grand  scheme 
widened  before  his  enraptured  vision.  So  also  if  we 
consider  solely  the  intellectual  aspects  of  the  Chris- 
tian system,  where  in  literature  shall  we  find  a  power 
of  deductive  reasoning  comparable  with  that  of  the 
great  apostle  to  the  Gentiles,  whose  boast  was  "  Not 
as  though  I  had  already  attained,  either  were  already 
perfect,  but  I  follow  after."  Pressing  this  analogy 
still  further,  we  may  not  inaptly  compare  theological 
systems  with  the  deductions  of  science,  and  like  the 
last  those  also  must  abide  the  test  of  experience,  and 
be  judged  by  the  united  voice  of  that  great  multitude 
who  have  been  redeemed  to  God  "  out  of  every 
kindred  and  tongue  and  people  and  nation." 

I  have  quite  failed  in  one  of  my  chief  aims  in  these 

lectures  if  I  have  not  succeeded  in  impressing  you 
21 


312  SENSE  OF  LIMITATION. 

with  the  strong  sense  which  I  feel  of  the  uncertainties 
and  limitations  which  encompass  the  student  of  na- 
ture on  every  side.  I  am  well  aware  that  such  feel- 
ings as  I  have  expressed  are  in  part  a  matter  of  tem- 
perament, and  that  some  men  are  more  susceptible 
to  such  impressions  than  others.  Still,  your  own 
knowledge  of  literature  will  sustain  me  in  the  asser- 
tion that  in  all  that  I  have  said  I  am  in  sympathy 
with  the  noblest  thinkers  the  world  has  known.  Un- 
numbered scholars,  of  whose  attainments  the  world 
has  been  proud,  and  for  whose  contributions  to  knowl- 
edge the  human  race  will  be  ever  grateful,  —  men  like 
Plato,  Marcus  Aurelius,  Copernicus,  Descartes,  New- 
ton, Faraday,  —  have  left  written  evidence  of  a  more 
or  less  deep  conviction  that  the  intellectual  life  has  a 
nobler  destiny  than  the  life  of  the  body ;  that  there 
may  be  modes  of  existence  of  which  'the  senses  take 
no  cognizance ;  and  that,  while  the  things  which  are 
seen  are  temporal,  the  things  that  are  unseen  are 
eternal.  There  has  always  been  with  such  minds  a 
"  reaching  forth  unto  those  things  which  are  before," 
and  although  they  may  not  have  recognized  the  goal, 
a  pressing  "toward  the  mark  for  the  prize  of  the 
high  calling  of  God  in  Christ  Jesus,  .  .  .  who 
shall  change  our  vile  body,  that  it  may  be  fashioned 
like  unto  His  glorious  body,  according  to  the  work- 
ing whereby  He  is  able  to  subdue  all  things  unto 
Himself." 

How  true  it  is  now  of  our  systems  of  theology  as  of 
our  systems  of  science  that  "  we  know  in  part,  and 
we  prophesy  in  part.  But  when  that  which  is  per- 
fect is  come,  then  that  which  is  in  part  shall  be  done 


man's  place  in  nature.  313 

away."  And  how  obviously  the  recognition  of  such 
limitations  in  our  present  life  points  beyond  the  veil. 
The  consciousness  of  limitation  is  an  evidence  of 
things  unseen,  and  thus  our  material  hindrances 
become  educators  of  faith.  They  are  a  law  in  our 
members  "  which  is  our  schoolmaster  to  bring  us 
unto  Christ." 

The  harmony  of  the  Christian  system  with  the 
methods  of  nature,  and  the  force  of  the  argument 
which  rests  on  this  analogy,  nowhere  appear  more 
conspicuously  than  when  studied  in  relation  to  the 
most  recent  of  the  great  systems  of  science.  Man  as 
an  animal  is  weak  as  compared  with  many  of  the 
higher  vertebrates,  and  unfitted  to  cope  with  them  in 
the  fight  for  existence.  Place  man  naked,  but  in  the 
full  command  of  his  physical  powers,  in  a  jungle  with 
tigers,  or  even  in  a  forest  with  wildcats,  and  he  would 
have  no  chance  in  the  inevitable  struggle  that  must 
ensue.  The  element  of  intelligence,  and  that  alone, 
makes  his  superiority;  and  this  mental  endowment 
has  made  a  comparatively  weak  animal  the  lord  of 
creation.  According  to  the  new  school  of  natural- 
ists, man's  development  must  have  begun  ages  back, 
when  intelligence  became  an  important  factor  in  the 
struggle  for  life.  Remember,  however,  that,  as  I  have 
before  shown,  this  factor  may  have  been  a  preor- 
dained condition  then  appearing  for  the  first  time  in 
the  chain  of  causation ;  and  that  as  yet  certainly  we 
have  no  knowledge  whatever  which  would  render 
such  an  interference  (if  the  preordained  can  be  called 
an  interference)  either  impossible  or  improbable; 
and  further,  recall  the  opinion  then  expressed  that 


314  man's  ancestors. 

geological  evidence  indicates  a  marked  break  at  the 
advent  of  man.  You  may  then  without  prejudice 
accept  the  necessary  inference  from  the  theory  that 
man  after  the  flesh  was  descended,  not  from  any 
species  now  existing,  but  from  some  species  far  less 
fitted  to  cope  with  its  surroundings  than  the  monkey, 
the  ourang,  or  the  gorilla  have  become.  These  an- 
thropoids are  not  regarded  as  the  ancestors  of  man ; 
but  both  they  and  man  are,  according  to  the  modern 
hypothesis,  descendants  of  a  common  ancestor.  Man 
has  remained  comparatively  feeble  in  his  physical 
powers,  but  has  gained  supremacy  through  his  in- 
telligence. The  animals  most  like  him  in  outward 
form  and  structure,  not  partaking  of  his  intelligence, 
have  been  developed  in  one  or  another  direction 
to  a  far  higher  degree ;  because  they  have  had  to 
wage  the  fight  for  existence  with  physical  powers 
alone. 

In  considering  the  influence  of  intelligence  in  the 
struggle  for  existence,  remember  that  it  has  led  men 
to  combine  in  societies,  and  establish  governments 
so  as  to  protect  the  weak.  Under  such  conditions, 
while  man's  collective  power  to  cope  with  brute 
forces  has  been  greatly  increased,  his  individual 
power  has  been  weakened ;  and  circumstances  con- 
stantly remind  us  what  a  weak,  miserable  animal  man 
is  when  left  to  his  own  resources.  When  you  con- 
sider what  a  delicate,  helpless  creature  the  human 
infant  is,  it  will  require  no  aid  of  poetry  or  art  to 
show  how  soon  the  race  would  be  extinguished  if  the 
human  mother  were  left  to  defend  her  offspring  with 
her  own  strength.     The  tales  of  the  wilderness  chiefly 


THE  LEADERS   OF  MEN.  315 

owe  their  interest,  as  it  seems  to  me,  to  the  vividness 
with  which  they  picture  the  features  of  that  fierce 
and  terrible  warfare  from  which  civilized  men  are  so 
greatly  protected  through  their  institutions  and  their 
inheritances ;  and  they  show  us  that  even  in  the  sav- 
age state  the  protection,  such  as  it  is,  arising  from 
association  and  combination,  is  equally  essential  to 
the  continued  life  of  the  race ;  thus  plainly  indicat- 
ing that  even  the  feeble  intelligence  of  the  savage 
gives  him  an  immense  advantage  over  the  brute  in 
the  struggle  for  existence. 

As  intelligence  has  been  the  chief  factor  which  has 
given  the  race  of  man  its  pre-eminence,  so  it  has  been 
that  gift  in  a  special  degree  which  has  given  to  indi- 
vidual men  the  power  of  advancing  their  race.  The 
great  men  who  have  marked  special  epochs  in  history, 
or  to  whom  great  movements  may  be  traced,  have 
been  men  of  great  mental  power  in  some  phase  or 
other,  or  else  men  endowed  with  unusually  clear 
spiritual  insight.  Recall  the  great  names  of  history, 
the  great  conquerors,  the  great  rulers,  the  great  law- 
givers, the  great  in  literature,  the  great  in  art,  the 
great  in  science,  the  great  in  philosophy,  the  great 
in  theology,  the  founders  of  states,  the  founders  of 
religions,  the  heroes,  the  saints,  and  the  prophets  of 
every  age.  Who  of  all  these  men  whose  names  are 
household  words,  remembered  and  cherished  when 
all  other  records  of  the  past  are  forgotten,  who,  I  say, 
has  exerted  the  greatest  influence,  and  produced  the 
most  lasting  effect  on  the  progress  of  mankind? 
There  can  be  but  one  answer.  Theorize  about  the 
matter  as  you  please,  explain  the  influence  as  you 


3 16    GROWTH  THE  METHOD  OF  CREATION. 

may,  by  far  the  greatest  effects  ever  produced  in  his- 
tory can  be  traced  directly  to  the  teaching  of  the  one 
Man  who  was  born  of  Mary  in  the  manger  at  Bethle- 
hem. Frame  what  theories  you  please  about  His 
nature,  He  is,  on  the  lowest  view  of  His  nature,  the 
greatest  leader  of  humanity.  It  is  the  reasonable 
course  to  accept  His  own  theory  of  Himself,  and  to 
act  upon  it;  and  men  by  acting  upon  it  have  raised 
themselves  and  their  fellows  immeasurably  in  the 
scale  of  being. 

Let  us  not  fail  to  remember  also  in  this  connection 
that  development,  or  slow  growth,  is  plainly  the 
method  of  creation.  Nothing  is  more  distinctly 
taught  by  nature  than  this.  Every  advance  in  knowl- 
edge only  makes  this  truth  more  plain.  Before  Dar- 
win published  his  now  famous  work  on  "  The  Origin 
of  Species,"  an  English  poet  wrote :  — 

"  The  solid  earth  whereon  we  tread 

"  In  tracts  of  fluent  heat  began, 

And  grew  to  seeming  random  forms, 
The  seeming  prey  to  cyclic  storms, 
Till  at  the  last  arose  the  man  ;  " 

and  this  plain  teaching  of  geology  can  be  supported 
by  overwhelming  facts  from  almost  every  department 
of  knowledge.  If  the  Bible  in  some  passages  may 
seem  to  imply  otherwise,  these  passages  must  be  in- 
terpreted by  the  spirit  of  the  writing,  which  through- 
out enforces  the  reverse  idea,  and  nowhere  more 
impressively  than  in  the  teaching  of  Christ  Himself. 
It  is  not,  as  some  seem  to  think,  a  question  of  power 
to  create,  but  solely  a  question  of  method.     One  of 


PERFECTION  THROUGH   SUFFERING.  317 

the  most  striking  features  in  the  life  of  Christ  is  His 
submission  to  the  slow,  halting,  and  apparently  cruel 
methods  of  nature ;  while  all  the  time  there  is  an  evi- 
dent consciousness  of  power  to  secure  the  end  and 
avoid  the  pain.  When  we  are  impatient  with  these 
methods,  and  think  that  they  derogate  from  the  maj- 
esty of  the  Almighty,  let  us  remember  that  scene 
under  the  olives  of  Gethsemane,  the  impatience  of 
the  disciple,  the  calmness  of  the  Master,  and  the 
memorable  words,  "  Thinkest  thou  that  I  cannot  now 
pray  to  my  Father,  and  He  shall  presently  give  me 
more  than  twelve  legions  of  angels  ?  " 

But  although  we  may  not  without  exaggeration 
push  our  analogy  further,  yet  we  can  catch  glimpses 
of  a  meaning  still  deeper  than  any  we  have  as  yet 
grasped ;  and  I  hope  I  shall  be  pardoned  if  with 
deepest  reverence  I  allude  to  this  obscure  and  terri- 
ble significance.  We  recognize  the  struggle  for  exist- 
ence as  an  agency  in  nature,  and  the  naturalists 
discuss  its  effects  as  they  would  those  of  heat  or 
electricity.  But  do  they,  do  we,  realize  what  is  im- 
plied by  these  words  ?  They  cannot ;  for  they  would 
be  staggered  by  the  thought,  and  overwhelmed  by 
the  horror,  and  could  not  write  or  speak  so  coolly  if 
they  did.  "  For  we  know  the  whole  creation  groaneth 
and  travaileth  in  pain  together  until  now."  Those 
who  minister  in  the  slums  of  your  cities  know  how 
true  this  is ;  and  they  will  tell  you  that  these  impas- 
sioned words  of  St.  Paul  convey  no  adequate  con- 
ception of  the  reality.  Even  fiction  does  not  dare 
to  depict  faithfully  the  terrible  death  struggle,  and 
art  is  powerless   before  it.     If  we  turn  pale  at  the 


3  IS  PERFECTION   THROUGH   SUFFERING. 

bare  recital  of  the  horrors  of  the  siege  of  Jerusalem, 
of  the  plague  at  Florence,  of  the  hecatombs  at  Co- 
massie,  or  of  the  battle-fields  recorded  on  every  page 
of  history,  and  also  of  the  visitations  of  earthquake, 
shipwreck,  tornado,  and  pestilence,  which  at  times 
come  near  our  own  homes,  and  are  stirred  from  the 
inner  depths  of  our  souls  by  the  distant  roar  of  the 
conflict,  what  must  have  been  the  ordeal  through 
which  our  race  has  passed,  what  the  sorrow  and 
anguish  through  which  every  advance  has  been  won ! 
And  do  we  ourselves  realize  that  our  civilization, 
our  education,  our  well-being,  and  all  that  consti- 
tutes our  birthright  have  been  purchased  with  so 
much  blood? 

If  this  be  true  of  man,  the  most  favored  of  creat- 
ures, and  through  his  intelligence  the  most  capable 
of  protecting  himself,  we  can  readily  believe  the 
declaration  of  naturalists  that  the  destructiveness  of 
the  internecine  warfare  among  the  lower  animals  is 
wholly  beyond  the  power  of  imagination  to  conceive. 
Swift  destruction  is  the  rule,  —  life,  however  short,  the 
great  exception ;  and  one  is  astonished  by  the  enor- 
mous productiveness  of  nature  which  can  people  the 
earth  in  spite  of  such  a  drain.  All  naturalists  are 
agreed  that  it  is  this  wholesale  destructiveness  which 
alone  gives  efficacy  to  what  is  called  natural  selection. 
As  the  animal  is  higher  in  the  scale  of  being,  the 
destructiveness  is  less;  but  in  the  same  proportion 
the  suffering  is  greater  ;  and  among  men  the  capa- 
bility of  suffering  is  almost  a  measure  of  intellectual 
and  spiritual  growth.  As  then  in  the  struggle  for 
existence  perfection  is  reached  through  suffering,  so 


THE   MYSTERY   OF   PERSONALITY.  319 

in  the  spiritual  world  men  rise  to  higher  things 
through  sorrow  ;  and  though  as  they  rise  their  power 
of  suffering  is  increased,  yet  in  the  beauty  of  holiness 
their  sorrow  is  at  last  turned  into  joy.  "  Blessed  are 
they  that  mourn,  for  they  shall  be  comforted."  Thus 
the  Cross  becomes  the  type  of  perfect  character,  as 
well  as  the  type  of  deepest  sorrow ;  and  as  we  pass 
beneath  its  shadow,  nature  will  help  to  teach  us  the 
deep  significance  of  those  solemn  words,  "  And  if  I 
be  lifted  up  I  shall  draw  all  men  unto  me." 

On  the  quai  which  lines  the  banks  of  the  Loire  at 
Tours  stands  a  noble  statue,  erected  in  honor  of  the 
greatest  philosopher  France  has  ever  known;  who, 
although  he  thought  and  wrought  elsewhere,  and  died 
in  a  foreign  land,  was  born  in  Touraine.  On  the 
pedestal  is  engraved  simply 

"  RENE    DESCARTES  ;  " 

but  at  the  foot  of  the  statue  we  read,  as  from  the 
great  man's  lips, 

"COGITO,   ERGO   SUM." 

Most  beautifully  has  this  famous  aphorism  been  para- 
phrased by  the  great  English  poet  whose  verses  I 
have  several  times  quoted  because  nowhere  else  do 
I  find  so  forcible  an  expression  of  the  overpowering 
sense  of  natural  phenomena  which  weighs  on  my 
own  soul,  but  which  my  feeble  words  are  powerless 
to  reproduce :  — 

"  The  baby  new  to  earth  and  sky, 

What  time  his  tender  palm  is  pressed 


320  "  C0GIT0,   ERGO   SUM." 

Against  the  circle  of  the  breast, 
Has  never  thought  that  «  This  is  I.' 

"  But  as  he  grows  he  gathers  much, 
And  learns  the  use  of  '  I '  and  '  me ' ; 
And  finds  '  I  am  not  what  I  see, 
And  other  than  the  things  I  touch.'  " 

The  mystery  of  evil  and  the  mystery  of  suffering 
have  their  counterpart  in  the  mystery  of  personality. 
Science  has  not  shed  one  single  ray  to  lighten  the 
darkness  of  either  mystery.  We  have  faith  "that 
somehow  good  will  be  the  final  goal  of  ill."  We 
trust  that  Omniscience  and  Free  Will,  Omnipotence 
and  Sin,  Beneficence  and  Suffering,  will  one  day  be 
reconciled  to  our  intelligences ;  and  we  look  for  the 
explanation  to  those  awful  necessities  which  an  alli- 
ance of  the  spiritual  with  the  material  implies.  Still, 
amidst  all  this  darkness  our  analogy  does  not  wholly 
fail  us,  and  we  have  clear  indications  that  the  pro- 
visions of  Grace  are  of  a  piece  with  the  provisions 
of  material  nature. 

If  there  is  one  attribute  of  our  being  which  more 
than  any  other  marks  our  individual  existence,  it  is 
the  consciousness  of  personality ;  and  yet  that  entity 
which  thinks  and  wills  is  so  blended  with  our  material 
nature  that  we  cannot,  except  in  thought,  dissociate 
the  two.  The  conclusion  of  the  profoundest  analysis 
which  philosophy  can  make  is  still  expressed  in  the 
three  words  "  COGITO,  ERGO  SUM."  Nevertheless, 
this  personality  is  the  most  conspicuous  fact  in  all 
human  history,  and  every  attempt  of  false  science  or 
of  poetry  to  resolve  or  obscure  it,  has  been  wholly 


SPIRITUAL  LIFE.  32 1 


vain.  Personality,  with  its  free  will,  is,  then,  an  ele- 
mentary principle  of  nature ;  and  how  wonderfully  is 
Christianity  throughout  in  harmony  with  this  funda- 
mental truth.  The  great  object  of  the  Gospel  is  to 
purify  and  sanctify  the  sources  from  which  it  pro- 
ceeds, but  the  personal  will  is  always  left  free  and 
inviolate.  The  recorded  miracles  all  dealt  with  ma- 
terial nature.  Christ  never  constrained  a  human  will. 
When  He  knew  that  it  was  to  betray  Him,  and  a 
single  word  would  arrest  the  action,  He  allowed  it 
free  course;  and  in  the  final  passion  —  "then  said 
Jesus,  '  Father  forgive  them,  for  they  know  not  what 
they  do.'  " 

We  have  time  for  only  one  further  thought.  Man 
knows  nature  because  he  is  in  harmony  with  it;  man 
knows  spiritual  truth  in  the  same  way;  and  certitude 
in  either  case  rests  on  similar  evidence.  Such  are 
the  general  propositions  which  I  have  sought  to 
maintain  in  these  lectures.  We  have  to  thank  the 
evolutionists  for  a  plausible  explanation  of  the  first 
of  the  propositions,  and  they  will  not  object  if  we 
apply  the  same  principles  to  the  second.  A  simple 
cell,  at  first  only  slightly  sensitive  to  light,  has  devel- 
oped into  that  organ  of  wonderful  adaptations,  the 
eye.  By  the  survival  of  the  fittest,  each  advantage 
gained  has  been  held  and  handed  down;  and  thus 
the  organ  has  been  gradually  adjusted  to  the  environ- 
ment, and  fitted  to  give  to  the  mind  of  man  truthful 
information  about  external  objects  and  accurate  im- 
pressions of  the  beauties  of  the  outer  world.  So 
another  cell,  specially  sensitive  to  the  vibrations  of 
the  atmosphere,  by  associating  with  itself  other  sen- 


322  CONCLUSION. 


sitive  cells  and  bequeathing  every  small  gain  by 
which  the  resulting  structure  became  more  respon- 
sive to  the  tremors  of  sound,  has  grown  into  that 
other  organ,  not  less  wonderful,  through  which  the 
mind  receives  equally  faithful  impressions  of  har- 
mony, melody,  and  articulate  speech.  The  method 
by  which  these  results  have  been  worked  out  is, 
however,  a  question  of  no  importance  to  our  argu- 
ment, so  long  as  we  all  admit — as  all  do,  evolu- 
tionists with  the  rest  —  that  the  capacity  of  these 
organs  to  give  accurate  information  about  the  ex- 
ternal world  is  wholly  due  to  their  adaptation  to  the 
environment. 

But  if  man's  harmony  with  his  environment  physi- 
cally is  an  evidence  of  truth,  then  his  harmony  with 
his  environment  spiritually  must  be  equally  so.  If  a 
sensitive  nerve  can  be  trusted,  a  sensitive  conscience 
is  not  less  trustworthy;  otherwise  man's  mind  must 
have  grown  into  harmony  with  its  environment  in  one 
relation,  and  not  in  the  other.  If  when  man  longs  for 
beauty  and  harmony  the  impressions  which  flow  in 
through  the  eye  and  ear  are  to  be  trusted,  then  it 
must  be  that  when  in  his  higher  moods  he  yearns  for 
purity  and  righteousness  and  holiness,  the  assurances 
which  come  to  him  on  his  bended  knees  are  equally 
well-founded. 

Finally,  if  there  be  any  knowledge,  if  there  be  any 
truth,  if  there  be  any  certainty  in  this  mortal  state 
of  being,  if  there  be  any  consolation  in  the  past,  any 
satisfaction  in  the  present,  any  hope  in  the  future  of 
this  world,  it  is  only  to  be  found  in  the  spiritual  life 


CONCLUSION.  323 


of  man.  That  alone  is  permanent  amid  ceaseless 
change;  that  alone  is  satisfying  amid  constant  sati- 
ety; that  alone  is  comforting  amid  constant  disap- 
pointments; that  alone  is  sustaining  amid  constant 
suffering ;  that  alone  is  consoling  amid  constant  be- 
reavement; that  alone  is  assuring  in  the  presence 
of  death ;  that  alone  is  triumphant  in  the  confident 
hope  of  immortality.  And  if  I  have  been  able,  in 
however  imperfect  a  way,  to  make  more  evident  to 
your  understanding  that  our  power  of  apprehending 
spiritual  things,  our  discernment  of  righteousness, 
our  thirst  for  affection,  our  aspiration  after  purity, 
our  communion  with  holiness,  are  as  truly  evidences 
of  external  realities  as  any  impressions  of  our  senses ; 
and  further,  if  it  has  appeared  that  the  inductions 
based  on  the  experiences  of  our  spiritual  life  are 
just  as  authentic,  and  just  as  valid,  as  those  drawn 
from  material  phenomena,  —  then  I  have  accomplished 
the  object  at  which  alone  I  have  aimed  in  these 
lectures. 

I  am  well  aware  that  I  have  not  sounded  the  key- 
note of  theology  ;  but  this  was  not  my  office.  I  was 
intrusted  with  the  very  subordinate  task  of  sustaining 
the  harmony  of  the  refrain  in  which  alone  nature  can 
join  in  the  heavenly  song;  and  I  even  fear  that  I 
have  made  my  part  too  prominent. 

You  will  receive  commission  to  preach  the  glad 
tidings  of  a  risen  Lord,  and  no  more  noble  service 
can  man  render  on  earth.  If  I  have  in  any  measure 
helped  to  prepare  your  way,  it  is  all  that  I  could 
hope  to  accomplish.     You  are  intrusted  with  a  mes- 


324  CONCLUSION. 


sage  before  which  all  the  learning  of  the  world  must 
bow.  Proclaim  it  confidently  and  fearlessly,  not  in 
"  oppositions  of  science  falsely  so-called,"  but  in 
the  name  of  Him  who  alone  is  "  the  Way,  the  Truth, 
and  the  Life." 


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Princeton  Theological  Semmary-Speer  Library 


1    1012  01014  3016 


